If f(x) and g(x) are integrable functions then [ f(x)dx ] [ g(x)dx ]=

MHT CET 2026 Mathematics question

If and are integrable functions then

(A)
(B)
(C)Correct
(D)

Answer: (C)

Solution

Let and , so and . By the product rule \frac{d}{dx}(FG)=F'G+FG'=f(x)\int g(x)dx+g(x)\int f(x)dx. Integrating both sides, FG=\int\left[f(x)\int g(x)dx+g(x)\int f(x)dx\right]dx. This is the integration-by-parts identity in disguise.

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Question ID VK-098692