If $f(x)$ is an antiderivative of $\dfrac{x + 1}{\sqrt{x - 1}}$ with respect to $x$, then value of $f(5) - f(2)$ is...

The area (in sq. units) of the region bounded by the curve $y = 2x - x^2$ and the X-axis is...

The area (in square units) of the region bounded by the circle $x^2 + y^2 = 9$ and the parabola $y^2 \leq 8x$ is...

The differential equation of all lines where the length of the normal from the origin is p and the inclination of the normal is $\alpha$ is... (where p and $\alpha$ are arbitrary constants)