List of top Mathematics Questions on Definite Integral asked in CUET (UG)

If \[ \int_{0}^{1}(3x^2+2x+1)\,dx=k, \] then the value of \(k\) is:

Evaluate the definite integral using standard definite integral properties: \[ \int_{0}^{\frac{\pi}{2}} \frac{\sin^5 x}{\sin^5 x + \cos^5 x} \, dx \]

The value of \( \int_0^2 |x - 2| dx = \)

The value of the integral \( I = \int_{-3}^3 (x^3 - x) dx \) is

Evaluate: $\int_0^{\pi/2}\sin x \, dx$

Evaluate the integral $\int_0^1 \frac{a - bx^2}{(a + bx^2)^2} , dx$:

The value of the integral \( \int_{\ln 2}^{\ln 3} \frac{e^{2x} - 1}{e^{2x} + 1} \, dx \) is:

The value of \(\int\limits_{-1}^1x^2 [x] dx\) is:

The value of \(\int\limits_{-3}^2x^2 |2x| dx\) is:

The value of \(\int_0^3 |2x-6|dx\) is:

The value of \(\int_0^{\frac{\pi}{2}} log (\frac{5 + 4 sinx}{5 + 4 cosx})dx\) is:

The integral \(\int_0^1x(1-x)^n dx\) is equal to :

If \(I=\int_{0}^{4}  \frac{\sqrt{x}}{\sqrt{x}+\sqrt{4-x}}dx\), then 8\(I\) is:

Match List I with List II

List I		List II
A.	\(\int\limits^{\frac{\pi}{2}}_0\frac{\sin^{\frac{7}{2}}x}{\sin^{\frac{7}{2}}+\cos^{\frac{7}{2}}}dx\)	I.	\(\frac{\pi}{4}-\frac{1}{2}\)
B.	\(\int\limits_0^{\pi}\frac{x\sin x}{1+\cos^2x}dx\)	II.	0
C.	\(\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}}x\cos x\ dx\)	III.	\(\frac{\pi}{4}\)
D.	\(\int\limits_{-\frac{\pi}{4}}^{\frac{\pi}{4}}\sin^2x\ dx\)	IV.	\(\frac{\pi^2}{4}\)

Choose the correct answer from the options given below :

The value of \(\int_1^4|x-1|dx \)  is :

The value of the integral \(\int\limits_2^4 \frac{x}{x^2+1} dx\) is: