The Shell Method Volume of Revolution

Find the area bounded by the following curves/lines

$y = x + 1$

$y = 9 - x^2$

$x = -1$

$x = 2$

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 $[\frac{\pi}{4}, \frac{5\pi}{4}]$

Use the shell method to determine the volume of the solid formed by rotating the region about the y axis.

$y = x^2 + 2$

$y = 0$, $x = 0$, $x = 2$