JEE Main 2013MathematicsIndefinite IntegrationEasyMCQ

JEE Main 2013 — Indefinite Integration Question with Solution

JEE Main 2013 (07 Apr)

Question

If ∫f(x)dx=ψ(x), then ∫x5f(x3)dx, is equal to 

Choose an option

Show full solutionCorrect option: A
Correct answer
A13x3ψ(x3)−∫x2ψ(x3)dx+c

Step-by-step explanation

∫x5fx3dx =∫x3.x2fx3dx  

Applying integration by parts, we get

=x3∫x2fx3dx-∫ddxx3∫x2fx3dx

=13x3ψx3-∫x2ψx3dx+c, where c is the constant of integration.

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Indefinite Integration chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.

Solve interactively →

About this question

This is a previous-year question from JEE Main 2013, covering the Indefinite Integration chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.