JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Analyzing +4 | -1

Let

f(x)=\int \frac{\sqrt{x}}{(1+x)^2} d x \, (x \geq 0)

. Then,

f(3)-f(1)

is equal to

View answer and explanation

Correct option: C

\frac{\pi}{12}+\frac{1}{2}-\frac{\sqrt{3}}{4}

Option C (

\frac{\pi}{12}+\frac{1}{2}-\frac{\sqrt{3}}{4}

) is correct because after using the substitution

x = \tan^2 \theta

and evaluating the definite integral, we get the result in option C.

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