Let $f(0)=1, f(0.5)=\frac{5}{4}, f(1)=2, f(1.5)=\frac{13}{4}$ and $f(2)=5$. Using Simpson's rule,$\int_0^2 f(x) dx$ is equal to

Evaluate the definite integral $\int_0^3 [x] \, dx$,where $[x]$ denotes the greatest integer function.

$\int\limits_0^{\frac{\pi }{2}} \frac{dx}{\cos^6 x + \sin^6 x}$ is equal to:

If $\theta_{1}$ and $\theta_{2}$ are respectively the smallest and the largest values of $\theta$ in $(0, 2\pi) - \{\pi\}$ which satisfy the equation $2 \cot^{2} \theta - \frac{5}{\sin \theta} + 4 = 0$,then $\int_{\theta_{1}}^{\theta_{2}} \cos^{2} 3\theta \, d\theta$ is equal to

$\int_0^{\pi /2} {\sqrt {\cos \theta } {{\sin }^3}\theta } \,d\theta = $

$\int_0^\pi |\cos x| \, dx = $