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JEE Advanced 2014

JEE Main 2014 Mathematics question on Definite Integrals and Areas

Let f:[0,2]→Rf:[0,2] \to R be a function which is continuous on [0,2][0,2] and is differentiable on (0,2)(0,2) with f(0)=1f(0)=1. Let F(x)=∫0x2f(t) dtF(x) = \int_0^{x^2} f(\sqrt{t})\, dt, for x∈[0,2]x \in [0,2]. If F′(x)=f′(x)F'(x) = f'(x), ∀\forall x∈(0,2)x \in (0,2), then F(2)F(2) equals
  1. A.
    e2−1e^2 - 1
  2. B.
    e4−1e^4 - 1
  3. C.
    e−1e - 1
  4. D.
    e4e^4
Show answer

Correct option: B

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