$ \int_{0}^{\frac{\pi}{2}} \frac{dx}{1+\cos x} = $

$\int\limits_0^{\frac{\pi }{2}} \frac{dx}{1 + a^2 \sin^2 x}$ has the value :

The approximate value of $\int_{1}^{9} x^2 dx$ by using the trapezoidal rule with $4$ equal intervals is:

If $\phi(t)=\begin{cases} 1, & \text{for } 0 \leq t < 1 \\ 0, & \text{otherwise} \end{cases}$, then $\int_{-3000}^{3000} \left( \sum_{r'=2014}^{2016} \phi(t-r') \phi(t-2016) \right) dt$ is

Domain of definition of the function $f(x) = \int\limits_0^x \frac{dt}{\sqrt{x^2 + t^2}}$ is

For a real number $x$,let $[x]$ denote the greatest integer less than or equal to $x$. The smallest positive integer $n$ for which the integral $\int_{1}^{n} [x][\sqrt{x}] \, dx$ exceeds $60$ is