List of top Mathematics Questions on applications of integrals asked in MET

The area bounded by the curves \( y = \tan x,\ -\frac{\pi}{3} \le x \le \frac{\pi}{3} \), \( y = \cot x,\ \frac{\pi}{6} \le x \le \frac{\pi}{2} \) and the X-axis is:

The area of the region described by \( A = \{(x,y) : x^2 + y^2 \le 1 \text{ and } y^2 \le 1 - x \} \) is

The value of \(\lim_{x \to \infty} \left\{ \frac{a_1^{1/x} + a_2^{1/x} + .......... + a_n^{1/x}}{n} \right\}^x\) is

The area bounded by \( y = x|\sin x| \) and X-axis between \( x = 0 \) and \( x = 2\pi \) is

The area enclosed by the curves \( |y + x| \le 1 \), \( |y - x| \le 1 \) and \( 2x^2 + 2y^2 = 1 \) is