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Thread: Integration and volume help?

  1. #1
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    Integration and volume help?

    I need some help with a volume integration problem.

    y=x, y=(x)^1/2; about x=2

    I'm supposed to graph it, then find the area, and then the volume. I can get the graph, but then I get confused. Any help?
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    Quote Originally Posted by OhhCalculus View Post
    I need some help with a volume integration problem.

    y=x, y=(x)^1/2; about x=2

    I'm supposed to graph it, then find the area, and then the volume. I can get the graph, but then I get confused. Any help?
    What methods are you familiar with?
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  3. #3
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    Quote Originally Posted by OhhCalculus View Post
    I need some help with a volume integration problem.

    y=x, y=(x)^1/2; about x=2

    I'm supposed to graph it, then find the area, and then the volume. I can get the graph, but then I get confused. Any help?
    area ...

    \displaystyle A = \int_0^1 \sqrt{x} - x \, dx

    volume using cylindrical shells w/r to x ...

    \displaystyle V = 2\pi \int_0^1 (2-x)(\sqrt{x} - x) \, dx

    volume using washers w/r to y ...

    \displaystyle V = \pi \int_0^1 (2-y^2)^2 - (2 - y)^2 \, dy
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    I'm familiar with both, but for this assignment we have to use washer method. Thanks for the help. I ended up with π/5, is that remotely correct?
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    Quote Originally Posted by OhhCalculus View Post
    I'm familiar with both, but for this assignment we have to use washer method. Thanks for the help. I ended up with π/5, is that remotely correct?
    Not correct.
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  6. #6
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    Ohh, woops. I went back through and realized I completely messed up with foiling in the beginning. I redid it and got 8π/15, is that any closer? :/
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  7. #7
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    that's fine.
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