List of top Mathematics Questions on Definite Integral

The integral \( \int_{-1}^{1} (1 - |x|) \, dx \) is equal to :

Evaluate the definite integral: \[ \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} (\sin |x| + \cos |x|)_~dx \]

The value of \[ \int_{\alpha}^{\beta} \sqrt{(x-\alpha)(\beta-x)}\,dx, \qquad \alpha\ne\beta \] is

The limit \[ \lim_{n \to \infty} \frac{1}{\sqrt{n}} \left[ 1 + \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{3}} + \dots + \frac{1}{\sqrt{n}} \right] \]

The definite integral \[ \int_{\pi/2}^{\pi} \frac{\sin x - x \cos x}{x(x + \sin x)} \, dx \] equals

The value of the definite integral \(\int_0^{\pi/2} \frac{\sin x}{\sin x + \cos x} dx\) is:

Evaluate \[ \int_{0}^{\sqrt{\pi}} x\sin^{2}(x^{2})\,dx \]

The integral \(\int_{0}^{1} \cot^{-1}(1 + x + x^2) dx\) is equal to:

The value of \( \int_0^{20} (\sin 4x + \cos 4x) \, dx \) is equal to:

The value of the integral \[ \int_{-1}^{1}\left(\frac{x^3+|x|+1}{x^2+2|x|+1}\right)dx \] is equal to :

Let \(\int_{-2}^{2} (|\sin x| + |\cos x|) \, dx = 2(3 - \cos 2) + \beta\). Then \(\beta \sin \left( \frac{\beta}{2} \right)\) equals:

Let \([\,]\) denote the greatest integer function. Then the value of} \[ \int_{0}^{3}\left(\frac{e^x+e^{-x}}{[x]!}\right)dx \] 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 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:

$∫_{-\pi}^{\pi} \frac{2x(1+sinx)}{1+cos^2x}dx $ is equal to?

if  $∫_{-1}^1 \frac{cos \, \alpha x}{1+3^x} dx = \frac2{\pi} $ then $\alpha$ is

The value of $∫_0^{\frac{\pi}{4}} \frac{dx}{1+tanx} $