List of top Mathematics Questions on Definite Integral asked in VITEEE

Evaluate the integral \( \int_{0}^{\pi/2} \frac{\sin x}{\sin x + \cos x} \, dx \).

Find the value of the integral \( \int_{0}^{\pi/2} \frac{\sqrt{\sin x}}{\sqrt{\sin x} + \sqrt{\cos x}} \, dx \).

Evaluate \( \displaystyle \int_{0}^{\pi/2} \frac{\sqrt{\sin x}}{\sqrt{\sin x} + \sqrt{\cos x}} \, dx \).

Find the value of \( \displaystyle \int_{0}^{\pi/2} \frac{\sin x}{\sin x + \cos x}\,dx \).

At $t = 0$, the function $f \left(t\right) = \frac{sin\,t}{t}$ has

The value of integral $\int\limits_0^1 \, \sqrt{\frac{1-x}{1+x}}dx$ is

$\displaystyle\lim_{n\to\infty} \left[\frac{1}{1.2} + \frac{1}{2.3} + \frac{1}{3.4} + .... + \frac{1}{n\left(n+1\right)}\right] $ is equal to