The value of $x$ that satisfies the equation $\int_{\sqrt{2}}^x \frac{dt}{|t| \sqrt{t^2-1}} = \frac{\pi}{12}$ is

If $I = \int_0^{100\pi} \sqrt{1 - \cos 2x} \, dx$,then the value of $I$ is

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:

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

$\int_2^3 \frac{d x}{x^2-x}$ is equal to

If ${I_1} = \int_0^1 {2^{x^2}} dx$,${I_2} = \int_0^1 {2^{x^3}} dx$,${I_3} = \int_1^2 {2^{x^2}} dx$,and ${I_4} = \int_1^2 {2^{x^3}} dx$,then which of the following is true?

Using the Trapezoidal rule, find the approximate value of $\int_1^4 y \, dx$ based on the following data:

$x$	$1$	$2$	$3$	$4$
$y$	$0.7111$	$0.7222$	$0.7333$	$0.7444$

(in $.1833$)