JEE Main 2020MathematicsIndefinite IntegrationMediumMCQ

JEE Main 2020 — Indefinite Integration Question with Solution

JEE Main 2020 (05 Sep Shift 2)

Question

If∫cosθ5+7sinθ-2cos2θdθ=Aloge|B(θ)|+C, where C is a constant of integration, then B(θ)A can be:

Choose an option

Show full solutionCorrect option: D
Correct answer
D5(2sinθ+1)sinθ+3

Step-by-step explanation

I=∫cosθ2sin2θ+7sinθ+3dθ

sinθ=t  ⇒  cosθdθ=dt

=12∫1t2+72t+32dt=12∫1t+742-542dt=15ln2t+1t+3+c=15ln2sinθ+1sinθ+3+c

so A=15

B(θ)=5(2sinθ+1)sinθ+3

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About this question

This is a previous-year question from JEE Main 2020, 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.