Find the volume created by rotating the area bounded by the curvesy =

x2 − 4x + 4 and y = x about the line x = −1.

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- Dec 3rd 2007, 06:02 PMsingh1030calculus word problemFind the volume created by rotating the area bounded by the curvesy =

x2 − 4x + 4 and y = x about the line x = −1.

- Dec 3rd 2007, 06:09 PMJhevon
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?