JEE Main 2020MathematicsIndefinite IntegrationMediumMCQ

JEE Main 2020 — Indefinite Integration Question with Solution

JEE Main 2020 (09 Jan Shift 2)

Question

If ∫dθcos2θtan2θ+sec2θ= λtanθ+2logefθ+C where C is a constant of integration, then the ordered pair λ,fθ is equal to:

Choose an option

Show full solutionCorrect option: C
Correct answer
C-1,1+tanθ

Step-by-step explanation

∫sec2θ1+tan2θ1-tan2θ+2tanθ1-tan2θdθ

=∫sec2θ1-tan2θ1+tanθ2dθ

=∫sec2θ1-tanθ1+tanθdθ

Let tanθ=t⇒sec2θdθ=dt

=∫1-t1+tdt=∫-1+21+tdt

=-t+2ln1+t+C

=-tanθ+2ln1+tanθ+C

⇒λ=-1 and fθ=1+tanθ

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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.