JEE Main 2017MathematicsIndefinite IntegrationHardMCQ

JEE Main 2017 — Indefinite Integration Question with Solution

JEE Main 2017 (02 Apr)

Question

Let, In=∫tannxdxn>1 . If I4+I6=atan5x+bx5+c, then the ordered pair a,b, is equal to

Choose an option

Show full solutionCorrect option: B
Correct answer
B15,0

Step-by-step explanation

Given,  In=∫tannxdx

⇒I4+I6=∫tan4xdx+∫tan6xdx

⇒I4+I6=∫tan4xdx1+tan2xdx

⇒I4+I6=∫tan4xsec2xdx

Put, tanx=t⇒sec2xdx=dt

⇒I4+I6=∫t4dt

⇒I4+I6=t55+c, where c is the constant of integration.

⇒atan5x+bx5+c=tan5x5+c

∴ a=15& b=0

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About this question

This is a previous-year question from JEE Main 2017, 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.