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JEE Main2015MathematicsDefinite IntegrationActual

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

Options

  1. A3 2
  2. B3
  3. C1 2
  4. D3 2

Correct answer

B. 3

Step-by-step solution

∫ 0 s i n x f t d t =   3 2   x . Differentiating w.r.t x both the sides, f sin ⁡ x · cos ⁡ x =   3 2 Put x =   π   3 . 1 2 · f   3 2 = 3 2 f 3 2 = 3 .

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