Find the volume created by rotating the area bounded by the curvesy =
x2 − 4x + 4 and y = x about the line x = −1.
By the shell method, the volume is given by:
$\displaystyle V = 2 \pi \int_a^b (\mbox{radius})(\mbox{height})~dx = 2 \pi \int_a^b (1 + x)(f(x) - g(x))~dx$
here, $\displaystyle a$ and $\displaystyle b$ are the points of intersection of the two graphs. with $\displaystyle a \le b$. $\displaystyle f(x)$ is the upper function, and $\displaystyle g(x)$ is the lower function.
can you continue?