Average Value of a Function Problem

Find the area between the curves $y = x$ and $y = x^2$

Compute the area between $y = \sin{x}$ and $y = \cos{x}$ and the interval $[\frac{\pi}{4}, \frac{5\pi}{4}]$

Determine the volume of the solid generated by rotating the function about the x-axis on $[0,3]$

$y = \sqrt{9 - x^2}$

Determine the volume of the solid generated by rotating the function about the y-axis on $[0,4]$

$y = \sqrt{x}$