$$\int\limits_\pi ^{16\pi } {|\sin x|dx = } $$

The value of $$\mathop {\lim }\limits_{n \to \infty } \sum\limits_{r = 1}^n {{{{r^3}} \over {{r^4} + {n^4}}}} $$ is

The value of $$\int\limits_0^\pi {{{\sin }^{50}}x{{\cos }^{49}}x\,dx} $$ is

All values of a for which the inequality $$\frac{1}{\sqrt{a}} \int_\limits1^a\left(\frac{3}{2} \sqrt{x}+1-\frac{1}{\sqrt{x}}\right) \mathrm{d} x<4$$ is satisfied, lie in the interval