Let f : ( - 1 ,   1 ) → R be a continuous function. If ∫ 0 sin ⁡ x f ( t )   d t…

Let f:(-1, 1)→R be a continuous function. If ∫0sin⁡xf(t) dt=32x, then f32 is equal to:
  1. 32
  2. 3
  3. 12
  4. 32

Solution

∫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.

Asked in: JEE Main 2015 (11 Apr Online)

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