List of top Mathematics Questions on Definite Integral

If \(n\) is an odd natural number and \[ I_n=\int_0^1 e^x(x-1)^n\,dx \] then \( I_n+nI_{n-1} \) is equal to:
Evaluate \[ \int_{1/e}^{e^2} \left| \frac{\log_e x}{x} \right| \,dx \]
Evaluate \[ I=\int_{-2}^{0} \Big(x^3+3x^2+3x+3+(x+1)\cos(x+1)\Big)\,dx \]
The value of the integral $\int_{0}^{\pi / 2} \sqrt{\cos x \sin 2x} dx$ is equal to
The value of $\int_{-1}^{1} \frac{\log_e(1 + |x|)}{1 + |x|} dx$ is equal to
The value of \(\displaystyle \int_{0}^{1} \frac{t}{(t+1)^3}\,dt\) is equal to:
The value of \(\displaystyle \int_{0}^{2\pi} \frac{\sin 2x}{x(2\pi - x)}\,dx\) is equal to:
The value of \(\int_0^3 |3x^2 - 3| dx\) is equal to

\[ \int_{0}^{8} x^{\frac{5}{3}} \left(4 - x^{\frac{2}{3}}\right)^{\frac{3}{2}} \, dx = \ ? \] 

\(\int_0^2 |2x^2-9x+9|dx=\)
Let \[ f(x)=\int_{1}^{4}\log[x]\ dx, \] where \([x]\) denotes the greatest integer function. Then the value of \(f(x)\) is:
Evaluate $\int_0^{\pi/2} \sin^6 x \cos^4 x dx$
Evaluate $\lim_{n\to\infty} \frac{1}{n^2}\sum_{r=1}^n r e^{r/n}$
If \[ \int_0^1 (3x^2+2x+1)\,dx=k, \] then the value of \(k\) is
The value of the definite integral $\int_0^{\pi/2} \ln(\tan x) \, dx$ is:
The value of the definite integral $\int_0^{\pi/2} \frac{\sin^{3/2} x}{\sin^{3/2} x + \cos^{3/2} x} \, dx$ is:
Evaluate: \[ \int_0^1 x^3\ln(1+x)\,dx \]
Evaluate the definite integral: \( \int_{0}^{\pi/2} \sin^2(x) \, dx \).

Evaluate the definite integral: $\int_{0}^{2026} \frac{x^5}{x^5 + (2026 - x)^5} \, dx$

Evaluate the integral \[ \int_{0}^{\frac{\pi}{2}} \frac{3\sin x+4\cos x}{\sin x+\cos x}\,dx \]
If \( f(x) = \int_0^x t(\sin x - \sin t)dt \) then :
The value of $\int_{0}^{4} \sqrt{\frac{4-x}{4+x}} dx$ is:
Evaluate the definite integral: \( \displaystyle \int_{3}^{5} |x-4|\,dx \).
Evaluate the integral \( \int_{0}^{\pi/2} \frac{\sin x}{\sin x + \cos x} \, dx \).
Find the value of the integral \( \int_{0}^{\pi/2} \frac{\sqrt{\sin x}}{\sqrt{\sin x} + \sqrt{\cos x}} \, dx \).