# what is the volume of the solid generated by rotating about the y-axis & sinx

• Apr 13th 2010, 06:24 PM
yoman360
what is the volume of the solid generated by rotating about the y-axis & sinx
what is the volume of the solid generated by rotating about the y-axis the region enclosed by y=sinx and the x-axis, from x=0 to x=$\displaystyle \pi$.
• Apr 13th 2010, 06:32 PM
skeeter
Quote:

Originally Posted by yoman360
what is the volume of the solid generated by rotating about the y-axis the region enclosed by y=sinx and the x-axis, from x=0 to x=$\displaystyle \pi$.

cylindrical shells may be the way to go on this ...

what do you get for the integral set up to find the volume?
• Apr 13th 2010, 06:35 PM
eddie2042
Quote:

Originally Posted by yoman360
what is the volume of the solid generated by rotating about the y-axis the region enclosed by y=sinx and the x-axis, from x=0 to x=$\displaystyle \pi$.

Simply use the method of cylindrical shells:

$\displaystyle V = 2\pi\int_0^\pi x(\sin x)dx$

$\displaystyle V = 2\pi\left[sin x - xcos x\right]_0^\pi$

$\displaystyle V = 2\pi[\pi]$

$\displaystyle V = 2\pi^2$
• Apr 13th 2010, 06:38 PM
yoman360
Quote:

Originally Posted by eddie2042
Simply use the method of cylindrical shells:

$\displaystyle V = 2\pi\int_0^\pi x(\sin x)dx$

$\displaystyle V = 2\pi\left[sin x - xcos x\right]_0^\pi$

$\displaystyle V = 2\pi[\pi]$

$\displaystyle V = 2\pi^2$

Thanks I forgot about the cylindrical shells method and how to use it.