$\int_{\pi /4}^{\pi /2} \csc^2 x \, dx = $

$\int_{\pi /2}^{\pi} \frac{1 - \sin x}{1 - \cos x} \, dx =$

If $[2,6]$ is divided into four intervals of equal length,then the approximate value of $\int_2^6 \frac{1}{x^2-x} dx$ using Simpson's rule is

$\int_{0}^{\frac{\pi}{4}} \frac{\sin x+\cos x}{9+16 \sin 2 x} d x=k \log 3$,then $k=$

The velocity of a particle which starts from rest is given by the following table. The total distance travelled (in metre) by the particle in $10 \ s$, using the Trapezoidal rule, is:

$t \ (\text{in second})$	$0$	$2$	$4$	$6$	$8$	$10$
$v \ (\text{in m/s})$	$0$	$12$	$16$	$20$	$35$	$60$

If $I = \int_{0}^{\frac{\pi}{6}} \frac{\cos x}{x} dx$ and $J = \int_{\frac{\pi}{3}}^{\frac{\pi}{2}} \frac{\cos x}{x} dx$,which of the following is $CORRECT$?