JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

f(x)=\int e^x\left(\tan ^{-1}(x)+\frac{2 x}{\left(1+x^2\right)^2}\right) d x, f(0)=-1

then the value of

f(1)

is :

View answer and explanation

Correct option: A

\left(\frac{\pi}{4}-\frac{1}{2}\right)

Option A is correct because the integral is solved using integration by parts and the initial condition is applied to find the constant of integration, leading to the value of f(1).

More Questions from INDEFINITE INTEGRATION

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\int \sin ^5 x \cos ^4 x d x=

f(x)

is differentibale and

\int\limits_{0}^{t^2} x f(x) d x=\frac{2}{5} t^5

then

f\left(\frac{4}{25}\right)

equals If

\int \frac{1-7 \cos ^2 x}{\sin ^7 x \cos ^2 x} d x=\frac{f(x)}{\sin ^7 x}+C

is equal to If

\int {e}^{{x}^2}\left(2-\frac{1}{{x}^2}\right) {de}={e}^{{x}^2} {f}({x})+{C}

and

{f}\left(\frac{1}{2}\right)=2

, then

f(1)

is equal to (where

{C}

is an arbitrary constant)

\int \frac{x^7}{\left(1-x^2\right)^5} d x

is equal to:

\int \,\frac{{a{x^3} + \,\,b{x^2} + c}}{{{x^4}}}\;\,dx

equals