JEE Main 2015MathematicsDefinite IntegrationHardMCQ

JEE Main 2015 — Definite Integration Question with Solution

JEE Main 2015 (11 Apr Online)

Question

Let f:(-1, 1)→R be a continuous function. If ∫0sin⁡xf(t) dt=32x, then f32 is equal to:

Choose an option

Show full solutionCorrect option: B
Correct answer
B3

Step-by-step explanation

∫0sinxftdt= 32 x.

Differentiating w.r.t x both the sides,

fsin⁡x·cos⁡x= 32

Put x= π 3.

12·f 32=32

f32=3.

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About this question

This is a previous-year question from JEE Main 2015, 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.