Let f'(x)=f(x) where f(0)=1. If f(x)+g(x)=x^2 then _0^1f(x)g(x) ,dx is equal to

JEE Advanced Mathematics question

Let where . If then is equal to

Answer: (B)

From we get . Using gives , so and . Then

- dx= dx- dx .

Integrating by parts twice: $ dx=e^

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Question ID VK-110080