Mathematics › Definite Integration
Definite Integration Questions
397 questions across 11 subtopics — with step-by-step solutions.
Definite Integration by Parts(24)
- The value of | Mathematics | TestHub
- Let be a continuous function such that for... | Mathematics | TestHub
- The integral is equal to : | Mathematics | TestHub
- The value ofis ____________ | Mathematics | TestHub
- Letfor allThen the correct expression(S) i... | Mathematics | TestHub
- Letbe a thrice differentiable function. Su... | Mathematics | TestHub
- The value of the integral | Mathematics | TestHub
- The value of the integral | Mathematics | TestHub
- The value of the integralis | Mathematics | TestHub
- Let be a differentiable function such that... | Mathematics | TestHub
- The value of the integralis equal to: | Mathematics | TestHub
- If, then | Mathematics | TestHub
- Letwhere. Iffor natural numbersand, theneq... | Mathematics | TestHub
- If, thenis equal to _______. | Mathematics | TestHub
- Letbe a differentiable function such thata... | Mathematics | TestHub
- LetThen | Mathematics | TestHub
- If, whereandare coprime natural numbers, t... | Mathematics | TestHub
- The value of | Mathematics | TestHub
- For, let. If ,, thenis equal to | Mathematics | TestHub
- The value of the integralis equal to | Mathematics | TestHub
- Ifbe the orthocentre of the triangle whose... | Mathematics | TestHub
- Ifbe the orthocentre of the triangle whose... | Mathematics | TestHub
- Letbe a thrice differentiable function in.... | Mathematics | TestHub
- Let be a twice differentiable function suc... | Mathematics | TestHub
Definite Integration by Substitution(49)
- If , then is | Mathematics | TestHub
- If and then the value of is | Mathematics | TestHub
- Match the integrals in Column I with the v... | Mathematics | TestHub
- For , the value of | Mathematics | TestHub
- The following integralis equal to | Mathematics | TestHub
- If for , then is equal to: | Mathematics | TestHub
- Ifwheretakes only principal values, then t... | Mathematics | TestHub
- If and ; then | Mathematics | TestHub
- The value of integral is | Mathematics | TestHub
- The value of the integralis | Mathematics | TestHub
- If, then the value ofis | Mathematics | TestHub
- The integral equals: | Mathematics | TestHub
- If, then the value ofis | Mathematics | TestHub
- The integralis equal to | Mathematics | TestHub
- The integralis equal to | Mathematics | TestHub
- The integralis equal to | Mathematics | TestHub
- Ifandbe respectively the smallest and the... | Mathematics | TestHub
- Iffor allwhereandare fixed positive real n... | Mathematics | TestHub
- The integralis equal to: | Mathematics | TestHub
- If the value of the integralis, thenis equ... | Mathematics | TestHub
- Iffor allwhereandare fixed positive real n... | Mathematics | TestHub
- The integralequals : | Mathematics | TestHub
- The value of the integralis: | Mathematics | TestHub
- For, if, thenis equal to | Mathematics | TestHub
- If, for, and, thenequals ________. | Mathematics | TestHub
- If, whereare integers, thenis equal to | Mathematics | TestHub
- If, thenis equal to | Mathematics | TestHub
- Consider the equation.Which of the followi... | Mathematics | TestHub
- The integralis equal to ______. | Mathematics | TestHub
- The integralis equal to: | Mathematics | TestHub
- If, then | Mathematics | TestHub
- The value of the integralis equal to | Mathematics | TestHub
- Letbe a differentiable function satisfying... | Mathematics | TestHub
- The value of the integralis equal to | Mathematics | TestHub
- The value ofis equal to | Mathematics | TestHub
- The integralis equal to | Mathematics | TestHub
- The value ofis equal to | Mathematics | TestHub
- Let . If then is equal to : | Mathematics | TestHub
- Ifwhereandare co-prime thenis equal to ___... | Mathematics | TestHub
- The value of the integralis equal to | Mathematics | TestHub
- Let . Then and are the roots of the equati... | Mathematics | TestHub
- For, ifandthenis equal to | Mathematics | TestHub
- Let . Then and are the roots of the equati... | Mathematics | TestHub
- is equal to | Mathematics | TestHub
- For, the value of the integralis : | Mathematics | TestHub
- For, ifandthenis equal to | Mathematics | TestHub
- Let for and . Then is equal to : | Mathematics | TestHub
- The integral \(80 \int_0^{\frac{\pi}{4}}\l... | Mathematics | TestHub
- For k \in N , let b_{k}=\int_{1}^{e} \frac... | Mathematics | TestHub
Derivatives (Newton- Leibnitz)(61)
- then equals | Mathematics | TestHub
- The value of is | Mathematics | TestHub
- If and , then | Mathematics | TestHub
- Let be a differentiable function having .... | Mathematics | TestHub
- Let be a differentiable function having .... | Mathematics | TestHub
- Let be a continuous function, which satisf... | Mathematics | TestHub
- Let be a non-negative function defined on... | Mathematics | TestHub
- For , define . Then has | Mathematics | TestHub
- Let be a differentiable function such that... | Mathematics | TestHub
- If , then equals | Mathematics | TestHub
- If , for all , then the value of is | Mathematics | TestHub
- If , then is equal to | Mathematics | TestHub
- Letfor allbe a continuous function. Forifi... | Mathematics | TestHub
- Forifis a differentiable function such tha... | Mathematics | TestHub
- Ifthen | Mathematics | TestHub
- If, then | Mathematics | TestHub
- If, then | Mathematics | TestHub
- Ifis a differentiable function andthenis: | Mathematics | TestHub
- LetIfis minimum then the ordered pairis | Mathematics | TestHub
- Letbe a continuous and differentiable func... | Mathematics | TestHub
- Ifthenis | Mathematics | TestHub
- Letbe a continuous and differentiable func... | Mathematics | TestHub
- LetIfis minimum then the ordered pairis | Mathematics | TestHub
- Practice Question | Mathematics | TestHub
- , is equal to | Mathematics | TestHub
- Letbe a non-negative function inand twice... | Mathematics | TestHub
- Letbe a continuous function. Thenis equal to: | Mathematics | TestHub
- Letbe a differentiable function for all. T... | Mathematics | TestHub
- Letbe a non-negative function inand twice... | Mathematics | TestHub
- Letbe defined asIfis a differentiable func... | Mathematics | TestHub
- Letbe a twice differentiable function onsu... | Mathematics | TestHub
- Ifthenis | Mathematics | TestHub
- is equal to: | Mathematics | TestHub
- If the normal to the curveat a pointis par... | Mathematics | TestHub
- Let be a continuous function such that and... | Mathematics | TestHub
- Letbe a twice differentiable function on.... | Mathematics | TestHub
- Letbe a differentiable function in. If, th... | Mathematics | TestHub
- The minimum value of the twice differentia... | Mathematics | TestHub
- For, let. Then the minimum value of the fu... | Mathematics | TestHub
- Ifthenis equal to | Mathematics | TestHub
- Ifthenis equal to | Mathematics | TestHub
- Let a differentiable functionsatisfy. Then... | Mathematics | TestHub
- Let f be a continuous function satisfying.... | Mathematics | TestHub
- Letbe a differentiable function defined on... | Mathematics | TestHub
- is equal to | Mathematics | TestHub
- Let . Then at is equal to | Mathematics | TestHub
- Letandbe defined as. LetSum of square of t... | Mathematics | TestHub
- Letand. Ifthenis equal to: | Mathematics | TestHub
- Let for some function and . Then is equal to | Mathematics | TestHub
- Let . Then the numbers of local maximum an... | Mathematics | TestHub
- Let . If the range of is , then equals : | Mathematics | TestHub
- Let . Then the numbers of local maximum an... | Mathematics | TestHub
- Let . If the range of is , then equals : | Mathematics | TestHub
- Let \(f:(0, \infty) \rightarrow \mathbf{R}... | Mathematics | TestHub
- Let be a real valued continuous function d... | Mathematics | TestHub
- If f(x) is a differentiable function and \... | Mathematics | TestHub
- Let f(x) be twice differentiable function... | Mathematics | TestHub
- Let l_{1}=\lim _{x \rightarrow 0} \frac{1}... | Mathematics | TestHub
- If f(x) is continuous function and F(x)=\i... | Mathematics | TestHub
- Let be a differentiable function such that... | Mathematics | TestHub
- If f(x)=\int_{1 / x}^{\sqrt{x}} \cos t^{2}... | Mathematics | TestHub
Differentiation and integration of series(1)
General(23)
- A value ofsuch thatis | Mathematics | TestHub
- Ifthenis equal to | Mathematics | TestHub
- If for all real tripletsthenis equal to: | Mathematics | TestHub
- Letbe a quadratic polynomial with real coe... | Mathematics | TestHub
- The value of is: | Mathematics | TestHub
- The value offor which, is equal to _____. | Mathematics | TestHub
- If , then equal to | Mathematics | TestHub
- is equal to | Mathematics | TestHub
- Let be the point of intersection of the cu... | Mathematics | TestHub
- The integral is equal to : | Mathematics | TestHub
- Let . Then the numbers of local maximum an... | Mathematics | TestHub
- Let be a twice differentiable function suc... | Mathematics | TestHub
- Let be a positive function and and . Then... | Mathematics | TestHub
- Let the domain of the function be . If whe... | Mathematics | TestHub
- is equal to : | Mathematics | TestHub
- Let for some function and . Then is equal to | Mathematics | TestHub
- Let be a real valued continuous function d... | Mathematics | TestHub
- The integral is equal to: | Mathematics | TestHub
- Let . If the range of is , then equals : | Mathematics | TestHub
- , then is | Mathematics | TestHub
- If \int_{\log 2}^{x} \frac{d t}{\sqrt{e^{t... | Mathematics | TestHub
- The range of the function f(x)=\int_{1}^{x... | Mathematics | TestHub
- Statement-1: \int_{-1}^{3} \frac{d x}{x^{2... | Mathematics | TestHub
Miscellaneous/Mixed(39)
- If makes intercept of 2 and 0 unit on and... | Mathematics | TestHub
- Let . If then one of the possible values o... | Mathematics | TestHub
- If and then | Mathematics | TestHub
- Paragraph:Read the following passage and a... | Mathematics | TestHub
- Let and . Then which one of the following... | Mathematics | TestHub
- Let and , for , then | Mathematics | TestHub
- Paragraph:Consider the functions defined i... | Mathematics | TestHub
- Practice Question | Mathematics | TestHub
- The value(s) of is (are) | Mathematics | TestHub
- Let be a function defined on such that , f... | Mathematics | TestHub
- Practice Question | Mathematics | TestHub
- For (the set of all real numbers), , Then a = | Mathematics | TestHub
- Let, the functionbe defined asthen the val... | Mathematics | TestHub
- Letbe a continuous function. Ifthenis equa... | Mathematics | TestHub
- Letbe a function such thatand, for alland.... | Mathematics | TestHub
- The functionthat satisfies the conditionis : | Mathematics | TestHub
- LetandConsider a matrixwhere. Thenis : | Mathematics | TestHub
- LetandConsider a matrixwhere. Thenis : | Mathematics | TestHub
- For positive integer, define. Then, the va... | Mathematics | TestHub
- Letfor every. Then the sum of all the elem... | Mathematics | TestHub
- Letbe a real valued continuous function on... | Mathematics | TestHub
- Letand. If, thenis equal to ______ | Mathematics | TestHub
- If, thenis | Mathematics | TestHub
- Let,be a function which satisfies. Thenis... | Mathematics | TestHub
- Letand. Let. Then the integralis equal to | Mathematics | TestHub
- Let Then is equal to | Mathematics | TestHub
- The value of the integralis : | Mathematics | TestHub
- Let . If upto times) , then is equal to | Mathematics | TestHub
- The value of the integralis : | Mathematics | TestHub
- The minimum value of the functionis | Mathematics | TestHub
- Let and . Then is equal to : | Mathematics | TestHub
- Let . Then the value of is equal to________ | Mathematics | TestHub
- If the integralis equal to, thenis equal t... | Mathematics | TestHub
- Let . If , then equals____ | Mathematics | TestHub
- Let denote the largest integer less than o... | Mathematics | TestHub
- Statement-1: Let \mathrm{a}, \mathrm{b}, \... | Mathematics | TestHub
- Statement 1: Let f(x) be a continuous func... | Mathematics | TestHub
- Statement-1 : If f(x)=\int_{0}^{1}(x f(t)+... | Mathematics | TestHub
- \int_{0}^{\pi} \cos ^{-1}(\sin \mathrm{x})... | Mathematics | TestHub
Properties Involving Inequalities (Approximation)(6)
- Letfor allwithIfthen the possible values o... | Mathematics | TestHub
- The value ofthen | Mathematics | TestHub
- If, then | Mathematics | TestHub
- Which of the following inequalities is/are... | Mathematics | TestHub
- . Then | Mathematics | TestHub
- Let M=\int_{0}^{\frac{\pi}{2}} \sqrt{\sin... | Mathematics | TestHub
Properties of definite integration(188)
- is | Mathematics | TestHub
- is | Mathematics | TestHub
- is | Mathematics | TestHub
- If then is equal to | Mathematics | TestHub
- Let be a function satisfying with and be a... | Mathematics | TestHub
- The value of the integral is | Mathematics | TestHub
- The value of is | Mathematics | TestHub
- The value of is | Mathematics | TestHub
- The value of , is | Mathematics | TestHub
- is equal to | Mathematics | TestHub
- Match the following. | Mathematics | TestHub
- The value of the integral, is | Mathematics | TestHub
- is equal to | Mathematics | TestHub
- The value of the integral, is | Mathematics | TestHub
- The value of , where denotes the greatest... | Mathematics | TestHub
- Let , where . Then equals | Mathematics | TestHub
- The solution for of the equation is | Mathematics | TestHub
- denotes the greatest integer function, is... | Mathematics | TestHub
- If , , then | Mathematics | TestHub
- For any real number , let denotes the larg... | Mathematics | TestHub
- The value of is | Mathematics | TestHub
- The value of is | Mathematics | TestHub
- If is the greatest integer , then the valu... | Mathematics | TestHub
- The value of the integral , where [.] deno... | Mathematics | TestHub
- The value of the integral is | Mathematics | TestHub
- The value of is : | Mathematics | TestHub
- The value of is : | Mathematics | TestHub
- Statement - I : The value of the integral... | Mathematics | TestHub
- Paragraph: Given that for each , exists. L... | Mathematics | TestHub
- Paragraph: Given that for each , exists. L... | Mathematics | TestHub
- If [ ] denotes the greatest integer functi... | Mathematics | TestHub
- The integralequals | Mathematics | TestHub
- Match the following. List – I List – II(A)... | Mathematics | TestHub
- The integralequals | Mathematics | TestHub
- ForletThenis equal to | Mathematics | TestHub
- The option(s) with the value ofandthat sat... | Mathematics | TestHub
- The integralis equal to | Mathematics | TestHub
- Letbe a function defined by, whereis the g... | Mathematics | TestHub
- If, thenis equal to | Mathematics | TestHub
- The value ofis equal to | Mathematics | TestHub
- The value of the integralwheredenotes the... | Mathematics | TestHub
- If, thenis equal to | Mathematics | TestHub
- Letbe a differentiable function such thata... | Mathematics | TestHub
- The integralis equal to | Mathematics | TestHub
- The integralequals | Mathematics | TestHub
- The value of the integralis | Mathematics | TestHub
- Letbe two non-constant differentiable func... | Mathematics | TestHub
- The values ofis | Mathematics | TestHub
- The value of the integral (where denotes t... | Mathematics | TestHub
- Letandbe continuous functions onsuch thata... | Mathematics | TestHub
- The value of the integralequals | Mathematics | TestHub
- Letwhereis a non-zero even function. Ifthe... | Mathematics | TestHub
- The value ofis: | Mathematics | TestHub
- The value ofwheredenotes the greatest inte... | Mathematics | TestHub
- Ifthen findequals____ | Mathematics | TestHub
- Ifandthen the value of the integralis | Mathematics | TestHub
- The value ofis | Mathematics | TestHub
- The value of, wheredenotes the greatest in... | Mathematics | TestHub
- is equal to | Mathematics | TestHub
- Letanddenote the fractional part ofand the... | Mathematics | TestHub
- Letdenote the greatest integer less than o... | Mathematics | TestHub
- The value ofis equal to: | Mathematics | TestHub
- The integralis equal to | Mathematics | TestHub
- The value ofis : | Mathematics | TestHub
- Letand. Thenis equal to | Mathematics | TestHub
- The value offor which, is | Mathematics | TestHub
- The value offor which, is | Mathematics | TestHub
- Letdenote the greatest integer less than o... | Mathematics | TestHub
- Let , where is continuous function in such... | Mathematics | TestHub
- The value ofis | Mathematics | TestHub
- Letandbe two functions satisfyingandthen t... | Mathematics | TestHub
- Letbe a continuous function such thatfor a... | Mathematics | TestHub
- If the value of the integralwhereanddenote... | Mathematics | TestHub
- Ifis the greatest integerthenis equal to : | Mathematics | TestHub
- The value of the definite integralis | Mathematics | TestHub
- The value of the integralis ________. | Mathematics | TestHub
- Let , and be functions such that and , for... | Mathematics | TestHub
- If the integralwhereare integers anddenote... | Mathematics | TestHub
- The value ofwheredenotes the greatest inte... | Mathematics | TestHub
- Letbe a positive real number such thatwher... | Mathematics | TestHub
- For any real number, letdenotes the larges... | Mathematics | TestHub
- The value ofis : | Mathematics | TestHub
- LetwhereThen which one of the following is... | Mathematics | TestHub
- The value of the definite integralis equal... | Mathematics | TestHub
- Ifdenotes the greatest integer less than o... | Mathematics | TestHub
- The value of the integralis: | Mathematics | TestHub
- Let , and be functions such that and , for... | Mathematics | TestHub
- Which of the following statement is correc... | Mathematics | TestHub
- Ifrepresents the greatest integer function... | Mathematics | TestHub
- Letdenote the greatest integerThen the val... | Mathematics | TestHub
- is equal to | Mathematics | TestHub
- Consider the integral where denotes the gr... | Mathematics | TestHub
- Let , where is continuous function in such... | Mathematics | TestHub
- Ifwhereis the greatest integer less than o... | Mathematics | TestHub
- Ifthenis equal to | Mathematics | TestHub
- The value of the integral,wheredenotes the... | Mathematics | TestHub
- Consider the integral where denotes the gr... | Mathematics | TestHub
- The value ofis: | Mathematics | TestHub
- Ifdenotes the greatest integer, then the v... | Mathematics | TestHub
- Letdenote the greatest integer less than o... | Mathematics | TestHub
- , wheredenotes greatest integer less than... | Mathematics | TestHub
- The value of the integralis equal to ______. | Mathematics | TestHub
- The value ofis equal to | Mathematics | TestHub
- Letwheredenotes the greatest integer. Then... | Mathematics | TestHub
- The integral, wheredenotes the greatest in... | Mathematics | TestHub
- Ifdenotes the greatest integer, then the v... | Mathematics | TestHub
- The integral, wheredenotes the greatest in... | Mathematics | TestHub
- The value of the integralis equal to | Mathematics | TestHub
- The value of the integralis equal to | Mathematics | TestHub
- The greatest integer less than or equal tois | Mathematics | TestHub
- , whereis the greatest integer function, i... | Mathematics | TestHub
- , wheredenotes greatest integer less than... | Mathematics | TestHub
- Letbe continuous function satisfying, for... | Mathematics | TestHub
- is equal to: | Mathematics | TestHub
- For any real number , let denote the large... | Mathematics | TestHub
- Letdenote the greatest integer less than o... | Mathematics | TestHub
- Let. Thenis equal to ______. | Mathematics | TestHub
- The value ofis ______. | Mathematics | TestHub
- The value of the integralis : | Mathematics | TestHub
- Let the functionbe defined as, wheredenote... | Mathematics | TestHub
- Ifbe a continuous function satisfying, the... | Mathematics | TestHub
- Letdenote the greatest integer function. I... | Mathematics | TestHub
- Letdenote the greatest integer function. I... | Mathematics | TestHub
- The value ofis ______ | Mathematics | TestHub
- If, thenis equal to _____ . | Mathematics | TestHub
- If [denotes the greatest integer, then the... | Mathematics | TestHub
- Let [x] denote the greatest integer. Consi... | Mathematics | TestHub
- If, thenis equal to | Mathematics | TestHub
- If then is equal to _____. | Mathematics | TestHub
- If [denotes the greatest integer, then the... | Mathematics | TestHub
- Letdenote the greatest integer. Thenis equ... | Mathematics | TestHub
- Ifbe a continuous function satisfying, the... | Mathematics | TestHub
- Let the functionbe defined as, wheredenote... | Mathematics | TestHub
- Let be a function satisfying . Then is equ... | Mathematics | TestHub
- If the value of the integralthen the value... | Mathematics | TestHub
- is equal to ______. | Mathematics | TestHub
- If, whereare integers, thenequals __________ | Mathematics | TestHub
- The value of the integral is | Mathematics | TestHub
- The value ofis equal to: | Mathematics | TestHub
- Letbe a function defined byand,. If, then... | Mathematics | TestHub
- Let be the function defined by and let be... | Mathematics | TestHub
- Paragraph: Let be the function defined by... | Mathematics | TestHub
- If, whereandare rational numbers, thenis e... | Mathematics | TestHub
- The value of is : | Mathematics | TestHub
- If the value of the integral is . Then, a... | Mathematics | TestHub
- The value of is : | Mathematics | TestHub
- The integral is equal to : | Mathematics | TestHub
- Let , where is a continuous odd function.... | Mathematics | TestHub
- If, whereandare rational numbers, thenis e... | Mathematics | TestHub
- Letbe two functions defined byand. Then th... | Mathematics | TestHub
- If, whereandare rational numbers, thenis e... | Mathematics | TestHub
- The value, wheredenotes the greatest integ... | Mathematics | TestHub
- The value of the integralequals: | Mathematics | TestHub
- If, whereare rational numbers, thenis equa... | Mathematics | TestHub
- The value of the integral is | Mathematics | TestHub
- If , then the value of equals_________ | Mathematics | TestHub
- Letbe defined. Ifand, then the value ofequ... | Mathematics | TestHub
- If , where , then is equal to_________ | Mathematics | TestHub
- The integral is equal to | Mathematics | TestHub
- The value of is equal to | Mathematics | TestHub
- If then the value of is ____________. (Her... | Mathematics | TestHub
- The value of is | Mathematics | TestHub
- The integral is equal to : | Mathematics | TestHub
- Let [.] denote the greatest integer functi... | Mathematics | TestHub
- is equal to : | Mathematics | TestHub
- If , then equals | Mathematics | TestHub
- The integral is equal to: | Mathematics | TestHub
- If , where denotes the greatest integer fu... | Mathematics | TestHub
- Let be the point of intersection of the cu... | Mathematics | TestHub
- The integral is equal to | Mathematics | TestHub
- The value of is | Mathematics | TestHub
- Let be a positive function and and . Then... | Mathematics | TestHub
- Let the domain of the function be . If whe... | Mathematics | TestHub
- If , then equals : | Mathematics | TestHub
- Let be an increasing function such that fo... | Mathematics | TestHub
- The value of integral \int_{\pi / 6}^{\pi... | Mathematics | TestHub
- If \int_{n}^{n+1} f(x) d x=n^{2}+n, \foral... | Mathematics | TestHub
- If denotes the Greatest Integer Function (... | Mathematics | TestHub
- Given f(\mathrm{x})=\sin ^{3} \mathrm{x} a... | Mathematics | TestHub
- Statement-1: The function f(\mathrm{x})=\i... | Mathematics | TestHub
- \int_{0}^{1} \operatorname{Tan}^{-1}\left(... | Mathematics | TestHub
- assertion : \int_{-1}^{1}|x| \operatorname... | Mathematics | TestHub
- \int_{0}^{\pi} x f(\sin x) d x is equal to | Mathematics | TestHub
- \int_{0}^{2 \pi} x \ln \left(\frac{3+\cos... | Mathematics | TestHub
- \quad \int_{0}^{\infty}\left[2 e^{-x}\righ... | Mathematics | TestHub
- \int_{0}^{\frac{\pi}{4}}\left(\pi x-4 x^{2... | Mathematics | TestHub
- \int_{-2 \pi}^{2 \pi} \frac{\sin ^{6} x}{\... | Mathematics | TestHub
- The value of the integral \left|\int_{0}^{... | Mathematics | TestHub
Reduction formula(3)
Sum of series using definite integration(2)
Walli's Formula(1)
Practice Definite Integration on TestHub
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