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Math Help - Volume by Disks/Washers

  1. #1
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    Volume by Disks/Washers

    Having an issue with a volume problem, was hoping I could get some help, please. I've got everything figured out on this one, except the limits of integration:

    y=2, y=9-X^2 Rotated about y=-1

    Normally, I would figure out the points on intersection by setting

    9-X^2=2.

    Solving this gives me X= +/- Square Root of 7. But when I set my limits to [-sqrt_7,+sqrt_7] they were marked as wrong.

    What gives?
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  2. #2
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    Quote Originally Posted by jhcasey815 View Post
    Having an issue with a volume problem, was hoping I could get some help, please. I've got everything figured out on this one, except the limits of integration:

    y=2, y=9-X^2 Rotated about y=-1

    Normally, I would figure out the points on intersection by setting

    9-X^2=2.

    Solving this gives me X= +/- Square Root of 7. But when I set my limits to [-sqrt_7,+sqrt_7] they were marked as wrong.

    What gives?
    Hi jhcasey815,

    You could rotate the part of the curve above y=2 around the line y=-1,
    or the part of the curve between y=-1 and y=2.

    Are you sure which one it is?

    If you are rotating the top part above y=2,
    you can rotate from x=0 to x= \sqrt{7}
    and double, or rotate from x= -\sqrt{7} to \sqrt{7}

    Since the disc radii are 9-x^2-(-1)=10-x^2
    it's also possible to rotate 10-x^2 above y=3 about the x-axis, if you are rotating the top section.

    Do you have the full question?
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