JEE MATHEMATICS MCQ: DIFFERENTIATION

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Analyzing +4 | -1

f(x)=\int_0^x(f(t))^2 d t, f: R \rightarrow R

be differentiable function and

f(g(x))

is differentiable function at

x=a

, then

View answer and explanation

Correct option: A

g(x)

must be differentiable at

x=a

Option A (0) is correct because, after substitution, the integral becomes the integral of an odd function over a symmetric interval, which is zero.

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