The acute angle between the diagonals of a parallelogram whose vertices are $\mathrm{A}(2,-1)$, $B(0,2), C(2,3)$ and $D(4,0)$ is

The shortest distance between the line $y-x=1$ and the curve $x=y^2$ is

The equation of the circle passing through the point $(1,1)$ and having two diameters along the pair of lines $x^2-y^2-2 x+4 y-3=0$ is

$$ \int \sin ^5 x \mathrm{~d} x= $$