Integrals of Some Particular Functions is an important topic in the Mathematics section in WBJEE exam. Practising this topic will increase your score overall and make your conceptual grip on WBJEE exam stronger.
This article gives you a full set of WBJEE PYQs for Integrals of Some Particular Functions with explanations for effective preparation. Practice of WBJEE Mathematics PYQs including Integrals of Some Particular Functions questions regularly will improve accuracy, speed, and confidence in the WBJEE 2026 exam.
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WBJEE PYQs for Integrals of Some Particular Functions with Solutions
1.
The value of the integral $ \int\limits^2_{1}e^{x} \left(log_{e} \,x + \frac{x+1}{x}\right)dx$ is- $e^2(1 + log_e 2)$
- $e^2 - e$
- $e^2(1 + log_e 2) - e$
- $e^2 -e(1 + log_e 2)$
2.
The value of the integral $\int\limits^{\pi/2}_{0}\sin^{5}\, x\,dx$ is- $\frac{4}{15}$
- $\frac{8}{5}$
- $\frac{8}{15}$
- $\frac{4}{5}$
3.
If $[x]$ denotes the greatest integer less than or equal to $x$, then the value of the integral $\int\limits^{{2}}_{{0}}x^2 [x] dx$- $\frac{5}{3}$
- $\frac{7}{3}$
- $\frac{8}{3}$
- $\frac{4}{3}$
4.
If $\frac{d}{dx} \left\{f\left(x\right)\right\} = g\left(x\right)$, then $\int\limits^{b}_{a}$ $f (x)g(x)dx$ is equal to- $\frac{1}{2}\left[f^{2}\left(b\right)-f^{2}\left(a\right)\right]$
- $\frac{1}{2}\left[g^{2}\left(b\right)-g^{2}\left(a\right)\right]$
- $f(b) - f(a)$
- $\frac{1}{2}\left[f\left(b^{2}\right)-f\left(a^{2}\right)\right]$
5.
If \(\int \frac{dx}{(x+1)(x-2)(x-3)}=\frac{1}{k}log_e\left \{ \frac{|x-3|^3|x+1|}{(x-2)^4}\right \}+c\), then the value of k is- 4
- 6
- 8
- 12
6.
$\int\sqrt{1+\cos\,x}\,dx$ is equal to- $2\sqrt{2} \cos \frac{x}{2}+C$
- $2\sqrt{2} \sin \frac{x}{2}+C$
- $\sqrt{2} \cos \frac{x}{2}+C$
- $\sqrt{2} \sin \frac{x}{2}+C$
7.
The value of $I = \int \limits^ \frac{\pi}{4}_{0}\left(tan^{n+1} x\right)dx + \frac{1}{2} \int \limits^ \frac{\pi}{2}_{0} tan^{n-1} \left(x / 2\right)dx$ is equal to- $\frac{1}{n}$
- $\frac{n+2}{2n+1}$
- $\frac{2n-1}{n}$
- $\frac{2n-3}{3n -2}$
8.
$\int\limits_{0}^{1000} e^{x-\left[x\right]} dx$ is equal to- $\frac{e^{1000}-1}{e-1}$
- $\frac{e^{1000}-1}{1000}$
- $\frac{e-1}{1000}$
- $1000(e-1)$
9.
The value of $\int\limits_{0}^{\infty} \frac{dx}{\left(x^{2}+4\right)\left(x^{2}+9\right)}$ is- $\frac{\pi}{60}$
- $\frac{\pi}{20}$
- $\frac{\pi}{40}$
- $\frac{\pi}{80}$
10.
The value of the integral is equal to $\int\limits^{\frac{\pi}{3}}_{\frac{\pi}{6}} \frac{\left(sin\,x - xcos\, x\right)}{x\left(x+sin\,x\right)}dx$ is- $log_{e}\left(\frac{2\left(\pi+3\right)}{2\pi+3\sqrt{3}}\right)$
- $log_{e}\left(\frac{\pi+3}{2\left(2\pi+3\sqrt{3}\right)}\right)$
- $log_{e}\left(\frac{2\pi +3\sqrt{3}}{2\left(\pi +3\right)}\right)$
- $log_{e}\left(\frac{2\left(2\pi +3\sqrt{3}\right)}{\pi +3}\right)$
11.
Suppose $M=\int\limits_{0}^{\pi / 2} \frac{\cos x}{x+2} d x$, $N=\int\limits_{0}^{\pi / 4} \frac{\sin x \cos x}{(x+1)^{2}} d x$ Then, the value of $(M-N)$ equals- $\frac{3}{\pi+2}$
- $\frac{2}{\pi-4}$
- $\frac{4}{\pi-2}$
- $\frac{2}{\pi+4}$
12.
The value of the integral $\int\limits_{-a}^{a} \frac{xe^{x^2}}{1+x^{2}} dx $ is- $e^{a^2}$
- $0$
- $e^{-a^2}$
- $a$
13.
Let $S=\frac{2}{1} ^{n}C_{0}+\frac{2^{2}}{2} ^{n}C_{1}+\frac{2^{3}}{3} ^{n}C_{2}+ ...... +\frac{2^{n+1}}{n+1} ^{n}C_{n}$. Then $S$ equals- $\frac{2^{n+1}-1}{n+1}$
- $\frac{3^{n+1}-1}{n+1}$
- $\frac{3^n-1}{n}$
- $\frac{2^{n}-1}{n}$
14.
Let $f: R \rightarrow R$ be a continuous function which satisfies $f(x)=\int\limits_{0}^{x} f(t) d t$. Then, the value of $f\left(\log _{e} 5\right)$ is- 0
- 2
- -5
- 3
15.
If $I_{1} = \int\limits^{3\pi}_{0}f\left(\cos^{2}\,x\right)dx$ and $I_{2} = \int\limits^{\pi}_{0} f\left(\cos^{2}\,x\right)dx$, then- $I_1 = I_2$
- $3I_1 = I_2$
- $I_1 = 3I_2$
- $I_1 = 5I_2$
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