Definite Integration PYQs - Last 10 Years
WB JEE / Mathematics / Calculus / 61 recent questions
MathematicsCalculus2017-2026
Practice 61 WB JEE Mathematics questions from Definite Integration. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.
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Mathematics / Calculus
2017-2026
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31 in last 5 years61 in last 10 years
Last 10 Years Definite Integration Questions
Showing 50 of 61 filtered questions.
1Definite Integration
The least positive value of ' $a$ ' for which the equation $\int_0^x\left(t^2-8 t+13\right) d t=x \sin \frac{a}{x}$ has a solution is
MCQ+1 / -0.252026
2Definite Integration
Let $f(x)>0$ for all $x \in \mathbb{R}$ and $f(x)$ is bounded. If $\mathop {\lim }\limits_{n \to \infty } \sum_{r-1}^n a^{r-1} \int_{(r-1) a}^{r a} \frac{f(x) d x}{f(x)+f(2 r a-a-x)}=\frac{3}{5}$ where $0< a< 1$, then the value(s) of a is a...
MCQM+2 / -02026
3Definite Integration
Let $a, b, c$ be non-zero real numbers, such that $\int_0^r\left(1+\cos ^8 x\right)\left(a x^2+b x+c\right) d x=\int_0^{2^{\prime}}\left(1+\cos ^8 x\right)\left(a x^2+b x+c\right) d x$, then $a x^2+b x+c=0$ has
MCQ+2 / -0.52026
4Definite Integration
If $\int_0^1\left(\sum_{r=1}^{2013} \frac{x}{x^2+r^2}\right)\left(\prod_{r=1}^{2013}\left(x^2+r^2\right)\right) d x=\frac{1}{2}\left[\left(\prod_{r=1}^{2013}\left(1+r^2\right)-K^2\right]\right.$, then $K$ is
MCQ+1 / -0.252026
5Definite Integration
Let $f(x)$ be a real valued $f$ unction which is monotonic and differentiable. Then for any reals a and $b, \int_{f(a)}^{f(b)} 2 x\left\{b-f^{-1}(x)\right\} d x=$
MCQ+2 / -0.52026
6Definite Integration
The value of $\int\limits_{-100}^{100} \frac{\left(x+x^3+x^5\right)}{\left(1+x^2+x^4+x^6\right)} d x$ is
MCQM+2 / -02025
7Definite Integration
If $f(x)=\int\limits_0^{\sin ^2 x} \sin ^{-1} \sqrt{t} d t$ and $g(x)=\int\limits_0^{\cos ^2 x} \cos ^{-1} \sqrt{t} d t$, then the value of $f(x)+g(x)$ is
MCQM+2 / -02025
8Definite Integration
The value of the integral $\int_0^{\pi / 2} \log \left(\frac{4+3 \sin x}{4+3 \cos x}\right) d x$ is
MCQ+1 / -0.252025
9Definite Integration
$\int\limits_0^{1 \cdot 5}\left[x^2\right] d x$ is equal to
MCQ+1 / -0.252025
10Definite Integration
Let $f(x)=\max \{x+|x|, x-[x]\}$, where $[x]$ stands for the greatest integer not greater than $x$. Then $\int\limits_{-3}^3 f(x) d x$ has the value
MCQ+2 / -0.52025
11Definite Integration
$\int_\limits{-1}^1 \frac{x^3+|x|+1}{x^2+2|x|+1} d x$ is equal to
MCQ+1 / -0.252025
12Definite Integration
The value of the integral $\int\limits_3^6 \frac{\sqrt{x}}{\sqrt{9-x}+\sqrt{x}} d x$ is
MCQ+1 / -0.252025
13Definite Integration
\(\text { The points of extremum of } \int_\limits0^{x^2} \frac{t^2-5 t+4}{2+e^t} d t \text { are }\)
MCQM+2 / -02024
14Definite Integration
\(\lim _\limits{n \rightarrow \infty} \frac{1}{n^{k+1}}[2^k+4^k+6^k+\ldots .+(2 n)^k]=\)
MCQ+2 / -0.52024
15Definite Integration
Let \(\mathrm{I}(\mathrm{R})=\int_\limits0^{\mathrm{R}} \mathrm{e}^{-\mathrm{R} \sin x} \mathrm{~d} x, \mathrm{R}>0\). then,
MCQ+2 / -0.52024
16Definite Integration
Let \(f: \mathbb{R} \rightarrow \mathbb{R}\) be a differentiable function and \(f(1)=4\). Then the value of \(\lim _\limits{x \rightarrow 1} \int_\limits4^{f(x)} \frac{2 t}{x-1} d t\), if \(f^{\prime}(1)=2\) is
MCQ+1 / -0.252024
17Definite Integration
If \(\mathrm{f}(x)=\frac{\mathrm{e}^x}{1+\mathrm{e}^x}, \mathrm{I}_1=\int_\limits{\mathrm{f}(-\mathrm{a})}^{\mathrm{f}(\mathrm{a})} x \mathrm{~g}(x(1-x)) \mathrm{d} x\) and $$\mathrm{I}_2=\int_\limits{\mathrm{f}(-\mathrm{a})}^{\mathrm{f}(\m...
MCQ+1 / -0.252024
18Definite Integration
For any integer \(\mathrm{n}, \int_\limits0^\pi \mathrm{e}^{\cos ^2 x} \cdot \cos ^3(2 n+1) x \mathrm{~d} x\) has the value :
MCQ+1 / -0.252024
19Definite Integration
All values of a for which the inequality \(\frac{1}{\sqrt{a}} \int_\limits1^a\left(\frac{3}{2} \sqrt{x}+1-\frac{1}{\sqrt{x}}\right) \mathrm{d} x<4\) is satisfied, lie in the interval
MCQ+1 / -0.252024
20Definite Integration
Which of the following statements are true?
MCQM+2 / -02023
21Definite Integration
Let f be a non-negative function defined on \(\left[ {0,{\pi \over 2}} \right]\). If \(\int\limits_0^x {(f'(t) - \sin 2t)dt = \int\limits_x^0 {f(t)\tan t\,dt} } ,f(0) = 1\) then \(\int\limits_0^{{\pi \over 2}} {f(x)dx}\) is
MCQM+2 / -02023
22Definite Integration
The average ordinate of \(y = \sin x\) over \([0,\pi ]\) is :
MCQ+2 / -0.52023
23Definite Integration
\(\int\limits_0^{2\pi } {\theta {{\sin }^6}\theta \cos \theta d\theta }\) is equal to
MCQ+2 / -0.52023
24Definite Integration
If \({I_n} = \int\limits_0^{{\pi \over 2}} {{{\cos }^n}x\cos nxdx}\), then I\(_1\), I\(_2\), I\(_3\) ... are in
MCQ+1 / -0.252023
25Definite Integration
The value \(\int\limits_0^{1/2} {{{dx} \over {\sqrt {1 - {x^{2n}}} }}}\) is \((n \in N)\)
MCQ+1 / -0.252023
26Definite Integration
the expression \({{\int\limits_0^n {[x]dx} } \over {\int\limits_0^n {\{ x\} dx} }}\), where \([x]\) and \(\{ x\}\) are respectively integral and fractional part of \(x\) and \(n \in N\), is equal to
MCQ+1 / -0.252023
27Definite Integration
If I is the greatest of \({I_1} = \int\limits_0^1 {{e^{ - x}}{{\cos }^2}x\,dx}\), \({I_2} = \int\limits_0^1 {{e^{ - {x^2}}}{{\cos }^2}x\,dx}\), \({I_3} = \int\limits_0^1 {{e^{ - {x^2}}}dx}\), $${I_4} = \int\limits_0^1 {{e^{ - {x^2}/2}}dx...
MCQ+2 / -0.52022
28Definite Integration
Let \(f(x) = \int\limits_{\sin x}^{\cos x} {{e^{ - {t^2}}}dt}\). Then \(f'\left( {{\pi \over 4}} \right)\) equals
MCQ+1 / -0.252022
29Definite Integration
Let \(\mathop {\lim }\limits_{ \in \to 0 + } \int\limits_ \in ^x {{{bt\cos 4t - a\sin 4t} \over {{t^2}}}dt = {{a\sin 4x} \over x} - 1,\left( {0 < x < {\pi \over 4}} \right)}\). Then a and b are given by
MCQ+1 / -0.252022
30Definite Integration
The value of \(\int\limits_0^{{\pi \over 2}} {{{{{(\cos x)}^{\sin x}}} \over {{{(\cos x)}^{\sin x}} + {{(\sin x)}^{\cos x}}}}dx}\) is
MCQ+1 / -0.252022
31Definite Integration
Let f be derivable in [0, 1], then
MCQ+1 / -0.252022
32Definite Integration
Let \(f(x) = \left\{ {\matrix{
{0,} & {if} & { - 1 \le x \le 0} \cr
{1,} & {if} & {x = 0} \cr
{2,} & {if} & {0 < x \le 1} \cr
} } \right.\) and let \(F(x) = \int\limits_{ - 1}^x {f(t)dt}\), \(-\)1 \(\le\) x \(\le\) 1, then
MCQM+2 / -02021
33Definite Integration
Whichever of the following is/are correct?
MCQM+2 / -02021
34Definite Integration
Let \(I = \int_{\pi /4}^{\pi /3} {{{\sin x} \over x}dx}\). Then
MCQ+2 / -0.52021
35Definite Integration
If \(b = \int\limits_0^1 {{{{e^t}} \over {t + 1}}dt}\), then \(\int\limits_{a - 1}^a {{{{e^{ - t}}} \over {t - a - 1}}}\) is
MCQ+2 / -0.52021
36Definite Integration
Let f(x) be continuous periodic function with period T. Let \(I = \int\limits_a^{a + T} {f(x)\,dx}\). Then
MCQ+2 / -0.52021
37Definite Integration
The value of \(\int\limits_0^5 {\max \{ {x^2},6x - 8\} \,dx}\) is
MCQ+1 / -0.252021
38Definite Integration
If \(\int\limits_{{{\log }_e}2}^x {{{({e^x} - 1)}^{ - 1}}dx = {{\log }_e}{3 \over 2}}\), then the value of x is
MCQ+1 / -0.252021
39Definite Integration
The value of the integral \(\int\limits_{ - {1 \over 2}}^{{1 \over 2}} {{{\left\{ {{{\left( {{{x + 1} \over {x - 1}}} \right)}^2} + {{\left( {{{x - 1} \over {x + 1}}} \right)}^2} - 2} \right\}}^{1/2}}} dx\) is equal to
MCQ+1 / -0.252021
40Definite Integration
\(\int\limits_1^3 {{{\left| {x - 1} \right|} \over {\left| {x - 2} \right| + \left| {x - 3} \right|}}dx}\) is equal to
MCQ+1 / -0.252021
41Definite Integration
\(\int\limits_0^2 {[{x^2}]} \,dx\) is equal to
MCQ+1 / -0.252020
42Definite Integration
Let f, be a continuous function in [0, 1], then \(\mathop {\lim }\limits_{n \to \infty } \sum\limits_{j = 0}^n {{1 \over n}} f\left( {{j \over n}} \right)\) is
MCQ+1 / -0.252020
43Definite Integration
The value of \(\sum\limits_{n = 1}^{10} {} \int\limits_{ - 2n - 1}^{ - 2n} {{{\sin }^{27}}} x\,dx + \sum\limits_{n = 1}^{10} {} \int\limits_{2n}^{2n + 1} {{{\sin }^{27}}} x\,dx\) is equal to
MCQ+1 / -0.252020
44Definite Integration
The value of the integration \(\int\limits_{ - {\pi \over 4}}^{\pi /4} {\left( {\lambda |\sin x| + {{\mu \sin x} \over {1 + \cos x}} + \gamma } \right)} dx\)
MCQ+1 / -0.252019
45Definite Integration
\(\mathop {\lim }\limits_{n \to \infty } {3 \over n}\left[ {1 + \sqrt {{n \over {n + 3}}} + \sqrt {{n \over {n + 6}}} + \sqrt {{n \over {n + 9}}} + ... + \sqrt {{n \over {n + 3(n - 1)}}} } \right]\)
MCQ+1 / -0.252019
46Definite Integration
Let \({I_n} = \int\limits_0^1 {{x^n}} {\tan ^{ - 1}}xdx\). If \({a_n}{I_{n + 2}} + {b_n}{I_n} = {c_n}\) for all n \(\ge\) 1, then
MCQM+2 / -02019
47Definite Integration
The value of \(\mathop {\lim }\limits_{x \to 0} {1 \over x}\left[ {\int\limits_y^a {{e^{{{\sin }^2}t}}dt - } \int\limits_{x + y}^a {{e^{{{\sin }^2}t}}dt} } \right]\) is equal to
MCQ+1 / -0.252019
48Definite Integration
The value of the integral \(\int\limits_{ - 1}^1 {\left\{ {{{{x^{2015}}} \over {{e^{|x|}}({x^2} + \cos x)}} + {1 \over {{e^{|x|}}}}} \right\}} dx\) is equal to
MCQ+1 / -0.252019
49Definite Integration
The value of the integral \(I = \int_{1/2014}^{2014} {{{{{\tan }^{ - 1}}x} \over x}} dx\) is
MCQ+1 / -0.252018
50Definite Integration
If \(M = \int\limits_0^{\pi /2} {{{\cos x} \over {x + 2}}dx}\), \(N = \int\limits_0^{\pi /4} {{{\sin x\cos x} \over {{{(x + 1)}^2}}}dx}\), then the value of M \(-\) N is
MCQ+1 / -0.252018