If the integral Ι = ∫ e x 2 x 3 d x = e x 2 f x + c , where c is the constant of integration and f 1 = 0 , then the value of f 2 is equal to

Question

If the integral Ι = ∫ e x 2 x 3 d x = e x 2 f x + c , where c is the constant of integration and f 1 = 0 , then the value of f 2 is equal to, 4, 5 2, 3 2, 3

MARKS App · Accepted Answer

Let, x 2 = t ⇒ 2 x d x = d t ∴ Ι = ∫ e t ⋅ t 2 d t Using integration by parts, we get, Ι = 1 2 t e t - ∫ 1 ⋅ e t d t = 1 2 t e t - e t + c = e x 2 x 2 - 1 2 + c ∴ f x = x 2 - 1 2 ⇒ f 2 = 3 2

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