JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Medium

1 of 1

Application +4 | -1

Let

\int e^x\left(f(x)-f^{\prime}(x)\right) d x=\phi(x)

, then

\int e^x f(x) d x

is equal to

View answer and explanation

Correct option: C

\frac{1}{2}\left\{\phi(x)+e^x t(x)\right\}+c

Option C (

\frac{1}{2}\{\phi(x)+e^x t(x)\}

+c) is correct because by integrating

e^x(f(x)+f'(x))

and

e^x(f(x)-f'(x))

and adding them, we can isolate the integral of

e^x f(x)

More Questions from INDEFINITE INTEGRATION

Practice All Chapter MCQs →

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

f(x)

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

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

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

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

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

f(1)

{C}

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

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