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

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    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= \pi.
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    Quote Originally Posted by yoman360 View Post
    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= \pi.
    cylindrical shells may be the way to go on this ...

    what do you get for the integral set up to find the volume?
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    Quote Originally Posted by yoman360 View Post
    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= \pi.
    Simply use the method of cylindrical shells:

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

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

    V = 2\pi[\pi]

    V = 2\pi^2
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    Quote Originally Posted by eddie2042 View Post
    Simply use the method of cylindrical shells:

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

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

    V = 2\pi[\pi]

    V = 2\pi^2
    Thanks I forgot about the cylindrical shells method and how to use it.
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