List of top Mathematics Questions on Definite Integral asked in KEAM

The value of the integral \(\int_{0}^{\pi} \frac{\cos x}{1 + \sin^{2} x} \, dx\) is

If \( \int_{-\sqrt{3}}^{1} (-6x^2 + 18)\,dx = \alpha + \beta\sqrt{3} \), then the value of \( \alpha + \beta \) is equal to

The value of \( \int_{\pi/10}^{2\pi/5} \frac{\cot^3 x}{1+\cot^3 x}\,dx \) is equal to

\( \int_{0}^{1} \frac{3^{2x}}{3^x + 1}\,dx = \)