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WB JEE

Definite Integration

Mathematics

Previous Years Questions

MCQ (Single Correct Answer)

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If I is the greatest of $${I_1} = \int\limits_0^1 {{e^{ - x}}{{\cos }^2}x\,dx} $$, $${I_2} = \int\limits_0^1 {{e^{ - {x^...
WB JEE 2022
Let $$f(x) = \int\limits_{\sin x}^{\cos x} {{e^{ - {t^2}}}dt} $$. Then $$f'\left( {{\pi \over 4}} \right)$$ equals...
WB JEE 2022
Let $$\mathop {\lim }\limits_{ \in \to 0 + } \int\limits_ \in ^x {{{bt\cos 4t - a\sin 4t} \over {{t^2}}}dt = {{a\sin 4x...
WB JEE 2022
The value of $$\int\limits_0^{{\pi \over 2}} {{{{{(\cos x)}^{\sin x}}} \over {{{(\cos x)}^{\sin x}} + {{(\sin x)}^{\cos...
WB JEE 2022
Let f be derivable in [0, 1], then
WB JEE 2022
Let $$I = \int_{\pi /4}^{\pi /3} {{{\sin x} \over x}dx} $$. Then
WB JEE 2021
If $$b = \int\limits_0^1 {{{{e^t}} \over {t + 1}}dt} $$, then $$\int\limits_{a - 1}^a {{{{e^{ - t}}} \over {t - a - 1}}}...
WB JEE 2021
Let f(x) be continuous periodic function with period T. Let $$I = \int\limits_a^{a + T} {f(x)\,dx} $$. Then
WB JEE 2021
The value of $$\int\limits_0^5 {\max \{ {x^2},6x - 8\} \,dx} $$ is
WB JEE 2021
If $$\int\limits_{{{\log }_e}2}^x {{{({e^x} - 1)}^{ - 1}}dx = {{\log }_e}{3 \over 2}} $$, then the value of x is
WB JEE 2021
The value of the integral $$\int\limits_{ - {1 \over 2}}^{{1 \over 2}} {{{\left\{ {{{\left( {{{x + 1} \over {x - 1}}} \r...
WB JEE 2021
$$\int\limits_1^3 {{{\left| {x - 1} \right|} \over {\left| {x - 2} \right| + \left| {x - 3} \right|}}dx} $$ is equal to
WB JEE 2021
Let f, be a continuous function in [0, 1], then $$\mathop {\lim }\limits_{n \to \infty } \sum\limits_{j = 0}^n {{1 \over...
WB JEE 2020
$$\int\limits_0^2 {[{x^2}]} \,dx$$ is equal to
WB JEE 2020
The value of $$\sum\limits_{n = 1}^{10} {} \int\limits_{ - 2n - 1}^{ - 2n} {{{\sin }^{27}}} x\,dx + \sum\limits_{n = 1}^...
WB JEE 2020
The value of $$\int\limits_0^\pi {{{\sin }^{50}}x{{\cos }^{49}}x\,dx} $$ is
WB JEE 2011
The value of $$\mathop {\lim }\limits_{n \to \infty } \sum\limits_{r = 1}^n {{{{r^3}} \over {{r^4} + {n^4}}}} $$ is...
WB JEE 2011
$$\int\limits_\pi ^{16\pi } {|\sin x|dx = } $$
WB JEE 2011
The value of $$\int\limits_{ - 2}^2 {(x\cos x + \sin x + 1)dx} $$ is
WB JEE 2011
If $$I = \int\limits_0^1 {{{dx} \over {1 + {x^{\pi /2}}}}} $$, then
WB JEE 2010
The value of $$I = \int\limits_{ - \pi /2}^{\pi /2} {|\sin x|dx} $$ is
WB JEE 2010
If $${I_1} = \int\limits_0^{3\pi } {f({{\cos }^2}x)dx} $$ and $${I_2} = \int\limits_0^\pi {f({{\cos }^2}x)dx} $$, then...
WB JEE 2010
If $${d \over {dx}}\{ f(x)\} = g(x)$$, then $$\int\limits_a^b {f(x)g(x)dx} $$ is equal to
WB JEE 2010
The value of the integral $$\int\limits_0^{\pi /2} {{{\sin }^5}xdx} $$ is
WB JEE 2010
$$\int\limits_0^{1000} {{e^{x - [x]}}dx} $$ is equal to
WB JEE 2009
$$\int\limits_{ - 1}^4 {f(x)dx = 4} $$ and $$\int\limits_2^4 {\{ 3 - f(x)\} dx = 7} $$, then the value of $$\int\limits_...
WB JEE 2009
If $${I_1} = \int\limits_0^{\pi /4} {{{\sin }^2}xdx} $$ and $${I_2} = \int\limits_0^{\pi /4} {{{\cos }^2}xdx} $$, then...
WB JEE 2009
The value of $$\int\limits_0^\infty {{{dx} \over {({x^2} + 4)({x^2} + 9)}}} $$ is
WB JEE 2009
If $$f(x) = f(a - x)$$, then $$\int\limits_0^a {xf(x)dx} $$ is equal to
WB JEE 2009
The value of the $$\mathop {\lim }\limits_{n \to \infty } \left( {{1 \over {n + 1}} + {1 \over {n + 2}} + ... + {1 \over...
WB JEE 2008
The value of the integral $$\int\limits_{ - a}^a {{{x{e^{{x^2}}}} \over {1 + {x^2}}}dx} $$ is
WB JEE 2008
The value of $$\int\limits_{ - 3}^3 {(a{x^5} + b{x^3} + cx + k)dx} $$, where a, b, c, k are constants, depends only on...
WB JEE 2008
The value of $$\int\limits_0^\pi {|\cos x|dx} $$ is
WB JEE 2008
The value of the integral $$\int\limits_0^2 {|{x^2} - 1|dx} $$ is
WB JEE 2008
If $$h(x) = \int\limits_0^x {{{\sin }^4}t\,dt} $$, then $$h(x + \pi )$$ equals
WB JEE 2008
If $$I = \int\limits_{ - \pi }^\pi {{{{e^{\sin x}}} \over {{e^{\sin x}} + {e^{ - \sin x}}}}dx} $$, then I equals
WB JEE 2008
$$\int\limits_{ - \pi /2}^{\pi /2} {{{\sin }^9}x{{\cos }^5}x\,dx} $$ equals
WB JEE 2008

MCQ (More than One Correct Answer)

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Let $$f(x) = \left\{ {\matrix{ {0,} & {if} & { - 1 \le x \le 0} \cr {1,} & {if} & {x = 0} \cr {2,} & {if} &...
WB JEE 2021
Whichever of the following is/are correct?
WB JEE 2021

Subjective

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Prove that $$I = \int\limits_0^{\pi /2} {{{\sqrt {\sec x} } \over {\sqrt {\cos ecx} + \sqrt {\sec x} }}dx = {\pi \over...
WB JEE 2011
Evaluate the following integral $$\int\limits_{ - 1}^2 {|x\sin \pi x|dx} $$
WB JEE 2010
If m, n be integers, then find the value of $$\int\limits_{ - \pi }^\pi {{{(\cos mx - \sin nx)}^2}dx} $$
WB JEE 2009

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