The function $L(x) = \int_1^x \frac{dt}{t}$ satisfies the equation

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 $\int_0^b \frac{dx}{1+x^2} = \int_b^{\infty} \frac{dx}{1+x^2}$, then $b$ is equal to

If $\int_1^n [x] dx = 120$,then $n = $

$\int\limits_1^{\sqrt 2 } {\frac{{{x^2} + 1}}{{{x^4} + 1}}} \,dx$ is equal to:

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