For any integer $$n$$ the integral ...........
$$\int\limits_0^\pi {{e^{{{\cos }^2}x}}{{\cos }^3}\left( {2n + 1} \right)xdx} $$ has the value

Evaluate the following : $$\,\,\int\limits_0^{\pi /2} {{{x\sin x\cos x} \over {{{\cos }^4}x + {{\sin }^4}x}}} dx$$

Sketch the region bounded by the curves $$y = \sqrt {5 - {x^2}} $$ and $$y = \left| {x - 1} \right|$$ and find its area.

Plank' constant has dimension __________.