If m, n be integers, then find the value of $$\int\limits_{ - \pi }^\pi {{{(\cos mx - \sin nx)}^2}dx} $$

Evaluate the following integral $$\int\limits_{ - 1}^2 {|x\sin \pi x|dx} $$

Prove that $$I = \int\limits_0^{\pi /2} {{{\sqrt {\sec x} } \over {\sqrt {\cos ecx} + \sqrt {\sec x} }}dx = {\pi \over 4}} $$