JEE Main 2017MathematicsDefinite IntegrationMediumMCQ

JEE Main 2017 — Definite Integration Question with Solution

JEE Main 2017 (08 Apr Online)

Question

The integral ∫π12π48cos2xtanx+cotx3dx equals

Choose an option

Show full solutionCorrect option: D
Correct answer
D15128

Step-by-step explanation

Given

∫π12π48cos2xtanx+cotx3dx=∫π12π48cos2xsinxcosx+cosxsinx3dx

=∫π12π4cos2x1sin2x3=∫π12π4cos2x·sin2x·sin22xdx

=14∫π12π4sin4x·(1−cos4x)dx

=14∫π12π4sin4x-18∫π12π4sin8x

=−116cos4xπ12π4+18×8cos8xπ12π4

=−116−1−12+1641+12

=15128.

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About this question

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