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Math Help - [SOLVED] Volume between two curves

  1. #1
    T_C
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    [SOLVED] Volume between two curves

    Hi, I'm trying to figure out how to this question:

    The area bounded by the curves y = x^2, y = (x+2)^2 and the x-axis is rotated about the x-axis. Find the volume of the solid of revolution formed.

    Any help would be greatly appreciated. Thanks.
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  2. #2
    Member Last_Singularity's Avatar
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    Quote Originally Posted by T_C View Post
    Hi, I'm trying to figure out how to this question:

    The area bounded by the curves y = x^2, y = (x+2)^2 and the x-axis is rotated about the x-axis. Find the volume of the solid of revolution formed.

    Any help would be greatly appreciated. Thanks.
    Draw it out.

    You will find the intersection of the two parabola is at x = -1 and that the area bounded on either side of x = -1 are mirror images of each other.

    Use disc integration, where
    V = \pi \int_a^b f(x)^2 dx

    But since the region in -2<x<-1 is a mirror of the one at -1<x<0, you can simply integrate over the second region and multiply the volume by two: V = 2 \pi \int_{-1}^0 (x^2)^2 dx

    Essentially, what you are doing is taking the volume of a cylinder V = \pi h r^2 whose radius r varies. In this case, the radius is dependent on the parabola that you are integrating under (do you see it from your drawing)?
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  3. #3
    T_C
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    Thank you very much.

    Wow...the question was pretty simple. I already drew the graph and solved the equations simultaneously to get the intersection of the two parabolas before I asked the question, but the wording of the question confused me.

    Yeah I understood everything you said but I don't know what you mean by the cylinder thing.

    Thanks once again.
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