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

1. ## 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=$\displaystyle \pi$.

2. 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?

3. 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:

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

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

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

$\displaystyle V = 2\pi^2$

4. 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.

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### what is the volume of the solid generated by rotating about the y-axis the region enclosed by y=sinx

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