If f(x) = ^ -1 x 1-x^2 and g(x) = e^ ^ -1 x , then the value of f(x)g(x) ,dx = ...

MHT CET 2026 Mathematics question

If and , then the value of

Answer: (A)

. Put , so . The integral becomes \int te^t\,dt=te^t-\int e^t\,dt=e^t(t-1)+c. Hence the result is , option (A). Differentiating (A) gives

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Question ID VK-100042