WB JEE 2023 | Indefinite Integrals Question 16 | Mathematics

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)

WB JEE 2022

MCQ (Single Correct Answer)

-0.25

Let $$\int {{{{x^{{1 \over 2}}}} \over {\sqrt {1 - {x^3}} }}dx = {2 \over 3}g(f(x)) + c} $$ ; then

(c denotes constant of integration)

$$f(x) = \sqrt x ,g(x) = {x^{{3 \over 2}}}$$

$$f(x) = {x^{{3 \over 2}}},g(x) = {\sin ^{ - 1}}x$$

$$f(x) = \sqrt x ,g(x) = {\sin ^{ - 1}}x$$

$$f(x) = {\sin ^{ - 1}}x,g(x) = {x^{{3 \over 2}}}$$

WB JEE 2021

MCQ (Single Correct Answer)

-0.25

If $$\int {{{\sin 2x} \over {{{(a + b\cos x)}^2}}}dx} = \alpha \left[ {{{\log }_e}\left| {a + b\cos x} \right| + {a \over {a + b\cos x}}} \right] + c$$, then $$\alpha$$ is equal to

$${2 \over {{b^2}}}$$

$${2 \over {{a^2}}}$$

$$ - {2 \over {{b^2}}}$$

$$ - {2 \over {{a^2}}}$$

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