Volume Around y-axis with Cylindrical Shells

**shannon1111** · May 26th 2009, 05:38 PM

The region R enclosed by the curves y=8 x-23 and y=-x2+20 x-50 is rotated about the y-axis. Use cylindrical shells to find the volume of the resulting solid.

**Media_Man** · May 28th 2009, 05:49 PM

Okay, so $r(x)=8x-23$ and $R(x)=-x^2+20x-50$ Go ahead and set $r(x)=R(x)$ and you get your bounds of integration, $x=3\rightarrow9$ . The shell method states that $V=\int_a^b 2\pi x[R(x)-r(x)] dx = \int_3^9 2\pi x[(-x^2+20x-50)-(8x-23)] dx$ . Can you take it from there?

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