WBJEE PYQs for Integrals of Some Particular Functions with Solutions: Practice WBJEE Previous Year Questions

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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.

WBJEE PYQs for Integrals of Some Particular Functions with Solutions

1.
The value of the integral $\int\limits_{-a}^{a} \frac{xe^{x^2}}{1+x^{2}} dx $ is
- $e^{a^2}$
- $0$
- $e^{-a^2}$
- $a$
View Solution
2.
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
- $\frac{1}{n}$
- $\frac{n+2}{2n+1}$
- $\frac{2n-1}{n}$
- $\frac{2n-3}{3n -2}$
View Solution
3.
The value of $\int\limits_{0}^{\infty} \frac{dx}{\left(x^{2}+4\right)\left(x^{2}+9\right)}$ is
- $\frac{\pi}{60}$
- $\frac{\pi}{20}$
- $\frac{\pi}{40}$
- $\frac{\pi}{80}$
View Solution
4.
The value of the integral $\int\limits^{\pi/2}_{0}\sin^{5}\, x\,dx$ is
- $\frac{4}{15}$
- $\frac{8}{5}$
- $\frac{8}{15}$
- $\frac{4}{5}$
View Solution
5.
If $[x]$ denotes the greatest integer less than or equal to $x$, then the value of the integral $\int\limits^{{2}}_{{0}}x^2 [x] dx$
- $\frac{5}{3}$
- $\frac{7}{3}$
- $\frac{8}{3}$
- $\frac{4}{3}$
View Solution
6.
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
- $\frac{3}{\pi+2}$
- $\frac{2}{\pi-4}$
- $\frac{4}{\pi-2}$
- $\frac{2}{\pi+4}$
View Solution
7.
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
View Solution
8.
The value of the integral $ \int\limits^2_{1}e^{x} \left(log_{e} \,x + \frac{x+1}{x}\right)dx$ is
- $e^2(1 + log_e 2)$
- $e^2 - e$
- $e^2(1 + log_e 2) - e$
- $e^2 -e(1 + log_e 2)$
View Solution
9.
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
View Solution
10.
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
- $I_1 = I_2$
- $3I_1 = I_2$
- $I_1 = 3I_2$
- $I_1 = 5I_2$
View Solution
11.
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
- $\frac{1}{2}\left[f^{2}\left(b\right)-f^{2}\left(a\right)\right]$
- $\frac{1}{2}\left[g^{2}\left(b\right)-g^{2}\left(a\right)\right]$
- $f(b) - f(a)$
- $\frac{1}{2}\left[f\left(b^{2}\right)-f\left(a^{2}\right)\right]$
View Solution
12.
$\int\limits_{0}^{1000} e^{x-\left[x\right]} dx$ is equal to
- $\frac{e^{1000}-1}{e-1}$
- $\frac{e^{1000}-1}{1000}$
- $\frac{e-1}{1000}$
- $1000(e-1)$
View Solution
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
- $\frac{2^{n+1}-1}{n+1}$
- $\frac{3^{n+1}-1}{n+1}$
- $\frac{3^n-1}{n}$
- $\frac{2^{n}-1}{n}$
View Solution
14.
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
- $log_{e}\left(\frac{2\left(\pi+3\right)}{2\pi+3\sqrt{3}}\right)$
- $log_{e}\left(\frac{\pi+3}{2\left(2\pi+3\sqrt{3}\right)}\right)$
- $log_{e}\left(\frac{2\pi +3\sqrt{3}}{2\left(\pi +3\right)}\right)$
- $log_{e}\left(\frac{2\left(2\pi +3\sqrt{3}\right)}{\pi +3}\right)$
View Solution
15.
$\int\sqrt{1+\cos\,x}\,dx$ is equal to
- $2\sqrt{2} \cos \frac{x}{2}+C$
- $2\sqrt{2} \sin \frac{x}{2}+C$
- $\sqrt{2} \cos \frac{x}{2}+C$
- $\sqrt{2} \sin \frac{x}{2}+C$
View Solution

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WBJEE PYQs for Integrals of Some Particular Functions with Solutions

1.The value of the integral $\int\limits_{-a}^{a} \frac{xe^{x^2}}{1+x^{2}} dx $ is

2.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

3.The value of $\int\limits_{0}^{\infty} \frac{dx}{\left(x^{2}+4\right)\left(x^{2}+9\right)}$ is

4.The value of the integral $\int\limits^{\pi/2}_{0}\sin^{5}\, x\,dx$ is

5.If $[x]$ denotes the greatest integer less than or equal to $x$, then the value of the integral $\int\limits^{{2}}_{{0}}x^2 [x] dx$

6.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

7.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

8.The value of the integral $ \int\limits^2_{1}e^{x} \left(log_{e} \,x + \frac{x+1}{x}\right)dx$ is

9.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

10.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

11.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

12.$\int\limits_{0}^{1000} e^{x-\left[x\right]} dx$ is equal to

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

14.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

15.$\int\sqrt{1+\cos\,x}\,dx$ is equal to

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1.
The value of the integral $\int\limits_{-a}^{a} \frac{xe^{x^2}}{1+x^{2}} dx $ is

2.
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

3.
The value of $\int\limits_{0}^{\infty} \frac{dx}{\left(x^{2}+4\right)\left(x^{2}+9\right)}$ is

4.
The value of the integral $\int\limits^{\pi/2}_{0}\sin^{5}\, x\,dx$ is

5.
If $[x]$ denotes the greatest integer less than or equal to $x$, then the value of the integral $\int\limits^{{2}}_{{0}}x^2 [x] dx$

6.
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

7.
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

8.
The value of the integral $ \int\limits^2_{1}e^{x} \left(log_{e} \,x + \frac{x+1}{x}\right)dx$ is

9.
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

10.
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

11.
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

12.
$\int\limits_{0}^{1000} e^{x-\left[x\right]} dx$ is equal to

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

14.
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

15.
$\int\sqrt{1+\cos\,x}\,dx$ is equal to