If lt x → 0 ∫ 0 x ( x − s i n x ) a + t t 2 d t = 1 then the value of a is ____

lt x → 0 x − sin x ∫ 0 x a + t t 2 d t = 1 t a + x ( 1 − cos x ) x 2 = lt x → 0 a + x ( 2 sin 2 2 x ) x 2 = a 2 = 1 ⇒ a = 4

Mathematics - Definite Integration Question with Solution | TestHub

MathematicsDefinite IntegrationDerivatives (Newton- Leibnitz)Medium2 minQB

MathematicsMediuminteger

If $lt_{x \to 0} \int_{0}^{x} \frac{t ^{2} d t}{( x - s i n x ) a + t} = 1$ then the value of a is $____$

Answer:

Solution:

$lt_{x \to 0} \frac{\int _{0}^{x} \frac{t ^{2}}{a + t} d t}{x - sin x} = 1 t \frac{x ^{2}}{a + x ( 1 - cos x )} = lt_{x \to 0} \frac{x ^{2}}{a + x ( 2 sin ^{2} \frac{x}{2} )} = \frac{2}{a} = 1 \Rightarrow a = 4$

Stream:JEESubject:MathematicsTopic:Definite IntegrationSubtopic:Derivatives (Newton- Leibnitz)

⏱ 2mℹ️ Source: QB

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