$$\int {{{dx} \over {\cos x - \sin x}}} $$ is equal to

The eccentricity of an ellipse, with its centre at the origin, is $${1 \over 2}$$. If one of the directrices is $$x=4$$, then the equation of the ellipse is :

The value of $$\int\limits_{ - 2}^3 {\left| {1 - {x^2}} \right|dx} $$ is

If $$\int\limits_0^\pi {xf\left( {\sin x} \right)dx = A\int\limits_0^{\pi /2} {f\left( {\sin x} \right)dx,} } $$ then $$A$$ is