List of top Mathematics Questions on Definite Integral asked in UPSEE

$ \displaystyle \lim_{x \to 0} \frac{a^{\tan \, x} - a^{\sin \, x}}{\tan \, x - \sin \, x}$ is equal to $(a > 0)$

If $I = \int^\limits{\pi/4}_{0} (\sqrt{\tan \, x } + \sqrt{\cot \, x} ) dx $ then value of I is

Let $f(x) = \begin{cases} - 2 \sin x & \quad \text{if } x \leq - \frac{\pi}{2}\\ A \ \sin x + B & \quad \text{if } - \frac{\pi}{2} < x < \frac{\pi}{2} \\ \cos & \quad \text{if } x \leq \frac{\pi}{2} \end{cases} $ For what values of A and B, the function $f (x)$ is continuous throughout the real line ?