Questions in definite-integral

Select	Question
	$\int_{0}^{2n\pi }{\left( \|\sin x\|-\left. \left\| \frac{1}{2}\sin x \right. \right\| \right)}\ dx$ equals
	The value of $\int_{-a}^{a}{\frac{1}{x+{{x}^{3}}}dx}$ is
	$\int_{\pi /6}^{\pi /3}{\frac{dx}{1+\sqrt{\tan x}}=}$
	$\int_{\ -\pi }^{\pi }{\frac{{{\sin }^{4}}x}{{{\sin }^{4}}x+{{\cos }^{4}}x}\ dx}=$
	If f is continuous function, then
	The value of $\underset{n\to \infty }{\mathop{\lim }}\,\left[ \frac{n}{1+{{n}^{2}}}+\frac{n}{4+{{n}^{2}}}+\frac{n}{9+{{n}^{2}}}+....+\frac{1}{2n} \right]$is equal to
	$\underset{n\to \infty }{\mathop{\lim }}\,\frac{1}{{{1}^{3}}+{{n}^{3}}}+\frac{4}{{{2}^{3}}+{{n}^{3}}}+....+\frac{1}{2n}$is equal to
	$\underset{x\to a}{\mathop{\lim }}\,\frac{f(x)-f(a)}{g(x)\,-g(a)},$
	$\underset{n\to \infty }{\mathop{\lim }}\,{{\left[ \frac{n!}{{{n}^{n}}} \right]}^{1/n}}$ equals
	$\underset{n\to \infty }{\mathop{\lim }}\,\frac{1}{n}\sum\limits_{r=1}^{2n}{\frac{r}{\sqrt{{{n}^{2}}+{{r}^{2}}}}}$ equals