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