If ∫ 0 x 2 ( 1 + x ) f ( t ) d t = x , then the value of 10 f ( 2 ) must be

Differentiating both sides w.r.t. x , then f ( x 2 ( 1 + x ) ) × ( 2 x + 3 x 2 ) = 1 At x = 1 ⇒ f ( 2 ) = 5 1 ∴ 10 f ( 2 ) = 2

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MathematicsDefinite IntegrationDerivatives (Newton- Leibnitz)Easy2 minQB

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If $\int_{0}^{x^{2} (1 + x)} f (t) d t = x$ , then the value of $10 f (2)$ must be

Answer:

Solution:

Differentiating both sides w.r.t. $x$ , then

$f (x^{2} (1 + x)) \times (2 x + 3 x^{2}) = 1$

$At x = 1 \Rightarrow f (2) = \frac{1}{5} ∴ 10 f (2) = 2$

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

⏱ 2mℹ️ Source: QB

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