If ∫ f ( x ) d x = ψ ( x ) , then ∫ x 5 f ( x 3 ) d x , is equal to

∫ x 5 f x 3 d x = ∫ x 3 . x 2 f x 3 d x Applying integration by parts, we get = x 3 ∫ x 2 f x 3 d x - ∫ d d x x 3 ∫ x 2 f x 3 d x = 1 3 x 3 ψ x 3 - ∫ x 2 ψ x 3 d x + c , where c is the constant of integration.

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Mathematics - Indefinite Integration Question with Solution | TestHub

MathematicsIndefinite IntegrationBy partEasy2 minPYQ_2013

MathematicsEasysingle choice

If $\int f (x) d x = ψ (x)$ , then $\int x^{5} f (x^{3}) d x$ , is equal to

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Solution:

$\int x^{5} f (x^{3}) d x$ $= \int x^{3} . x^{2} f (x^{3}) d x$

Applying integration by parts, we get

$= x^{3} \int x^{2} f (x^{3}) d x - \int \frac{d}{d x} (x^{3}) \int x^{2} f (x^{3}) d x$

$= \frac{1}{3} x^{3} ψ (x^{3}) - \int x^{2} ψ (x^{3}) d x + c$ , where $c$ is the constant of integration.

Stream:JEESubject:MathematicsTopic:Indefinite IntegrationSubtopic:By part

⏱ 2mℹ️ Source: PYQ_2013

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