List of top Mathematics Questions on Some Properties of Definite Integrals asked in MET

\( \int_{0}^{\pi/2} \frac{\sin x - \cos x}{1 + \sin x \cos x} \, dx \) is equal to

The pair of lines \(\sqrt{3}x^2 - 4xy + \sqrt{3}y^2 = 0\) are rotated about the origin by \(\frac{\pi}{6}\) in the anticlockwise sense. The equation of the pair in the new position is

Let \[ I_1 = \int_{\alpha}^{\pi - \alpha} x \sin x \, dx, I_2 = \int_{\alpha}^{\pi - \alpha} f(\sin x) \, dx \] then \( I_2 \) is equal to:

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