JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Analyzing +4 | -1

Let

f(x)=\int \frac{x^2 d x}{\left(1+x^2\right)\left(1+\sqrt{\left(1+x^2\right)}\right)}

and

f(0)=0

. Then

f(1)

View answer and explanation

Correct option: B

\log (1+\sqrt{2})-\frac{\pi}{4}

The correct answer is B (

\log (1+\sqrt{2})-\frac{\pi}{4}

) because it is the result of evaluating the definite integral after finding the antiderivative and applying the initial condition f(0) = 0.

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