WB JEE 2011 | Indefinite Integrals Question 14 | Mathematics

PREVIOUS NEXT

WB JEE 2011

MCQ (Single Correct Answer)

-0.25

$$\int {{2^x}(f'(x) + f(x)\log 2)dx} $$ is

$${2^x}f'(x) + C$$

$${2^x}f(x) + C$$

$${2^x}(\log 2)f(x) + C$$

$$(\log 2)f(x) + C$$

WB JEE 2023

MCQ (Single Correct Answer)

-0.25

If $$I = \int {{{{x^2}dx} \over {{{(x\sin x + \cos x)}^2}}} = f(x) + \tan x + c} $$, then $$f(x)$$ is

$${{\sin x} \over {x\sin x + \cos x}}$$

$${1 \over {{{(x\sin x + \cos x)}^2}}}$$

$${{ - x} \over {\cos x(x\sin x + \cos x)}}$$

$${1 \over {\sin x(x\cos x + \sin x)}}$$

WB JEE 2023

MCQ (Single Correct Answer)

-0.25

If $$\int {{{dx} \over {(x + 1)(x - 2)(x - 3)}} = {1 \over k}{{\log }_e}\left\{ {{{|x - 3{|^3}|x + 1|} \over {{{(x - 2)}^4}}}} \right\} + c} $$, then the value of k is

WB JEE 2022

MCQ (Single Correct Answer)

-0.25

$$I = \int {\cos (\ln x)dx} $$. Then I =

$${x \over 2}\{ \cos (\ln x) + \sin (\ln x)\} + c$$ (c denotes constant of integration)

$${x^2}\{ \cos (\ln x) - \sin (\ln x)\} + c$$ (c denotes constant of integration)

$${x^2}\sin (\ln x) + c$$ (c denotes constant of integration)

$$x\cos (\ln x) + c$$ (c denotes constant of integration)

PREVIOUS NEXT

WB JEE Subjects