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Math Help - finding the volume

  1. #1
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    finding the volume

    im supposed to find the volume of the solid that results when the region enclosed by y = x^(1/2), y = 0 and x = 9. the region is revolved about the y = 3 line?

    well my intergral that i got for this problem is.

    V = pi*(the intergral of) (9 - y^(2))^(2) can someone tell me if the set up is right? basically i took the length of the strip to be my radius and then squared it times pi? thanks in advance...
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  2. #2
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    Since you are integrating with respect to y and the rotation is about a horizontal line (y=3), you should be using the cylindrical shells method.

    Alternatively, you could leave the function defined as y=\sqrt{x} and integrate with respect to x, and use the "discs" (aka "washers") method.
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  3. #3
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    so is my setup right? v equals the intergral of y*(9-y squared) with limits running from 0 to 3?
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  4. #4
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    Quote Originally Posted by slapmaxwell1 View Post
    so is my setup right? v equals the intergral of y*(9-y squared) with limits running from 0 to 3?
    Since you are revolving about the line y=3, the radius will be 3-y, not y.

    So:

    V = 2\pi \int_0^3 (3-y)(9-y^2)\,dy
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