JEE Main 2019MathematicsDefinite IntegrationMediumMCQ

JEE Main 2019 — Definite Integration Question with Solution

JEE Main 2019 (09 Jan Shift 2)

Question

If ∫0π/3tan⁡θ2k sec⁡θdθ=1-12, (k>0) , then the value of k is

Choose an option

Show full solutionCorrect option: C
Correct answer
C2

Step-by-step explanation

∫0π/3tan⁡x2ksec⁡xdx

=12k ∫0π/3sin⁡xcos⁡xdx

Put t=cos⁡x

dt= -sin⁡x dx, also x=0, t=1;x=π3, t=12

∴  12k ∫11/2-dtt

=12k∫1/21t-12 dt=12k×2 t121/21 

=2k 1-12=2-1k

Given 2-1k=1-12=2-12

∴k=2

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About this question

This is a previous-year question from JEE Main 2019, 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.