If A = ∫ 0 1 1 + t s i n t d t , find ∫ 4 π − 2 4 π 4 π + 2 − t s i n ( t /2 ) d t .

Put t = 2 x + 4 π − 2 . The integral becomes ∫ 0 1 sin ( x − 1 ) / ( 2 − x ) d x . Replacing x by 1 − x gives − ∫ 0 1 sin x / ( 1 + x ) d x = − A .

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Mathematics - Definite Integration Question with Solution | TestHub

MathematicsDefinite IntegrationDefinite Integration by SubstitutionHard2 minQB

MathematicsHardsingle choice

If $A = \int_{0}^{1} \frac{s i n t}{1 + t} d t$ , find $\int_{4 π - 2}^{4 π} \frac{s i n ( t /2 )}{4 π + 2 - t} d t$ .

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Answer:

Solution:

Put $t = 2 x + 4 π - 2$ . The integral becomes $\int_{0}^{1} sin (x - 1) / (2 - x) d x$ . Replacing $x$ by $1 - x$ gives $- \int_{0}^{1} sin x / (1 + x) d x = - A$ .

Stream:JEESubject:MathematicsTopic:Definite IntegrationSubtopic:Definite Integration by Substitution

⏱ 2mℹ️ Source: QB

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