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Math Help - Volume integral set-up

  1. #1
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    Volume integral set-up

    1) Consider the region R bounded by:

    x=4-y^2 and x=sqrt(4-y^2)

    Find the volume of the solid that results when R is rotated about the y-axis.

    2) Consider the region X bounded by:

    x=1, y=2-x, and y=2e^x

    Find the volume of the solid that results when X is rotated about the line x=2.

    I just need help setting up the integrals, I can easily compute them. Thanks a bunch!
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  2. #2
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    1)the equations given result into a parabola with vertex at(4,0) and a circle with radius 4 and centre at (0,0). so the region bounded by them is a point(correct me if i am wrong).so the volume will be 0.
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  3. #3
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    Quote Originally Posted by Pulock2009 View Post
    1)the equations given result into a parabola with vertex at(4,0) and a circle with radius 4 and centre at (0,0). so the region bounded by them is a point(correct me if i am wrong).so the volume will be 0.
    Actually, the second gives a circle of radius 2 with center at (0,0) but your point is still valid. Neither of the problems gives bounded region in the xy-plane to be rotated.

    Was there some additional condition, like x\ge 0 or y\ge 0?
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  4. #4
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    Quote Originally Posted by twittytwitter View Post
    1) Consider the region R bounded by:

    x=4-y^2 and x=sqrt(4-y^2)

    ...
    Have a look at the drawing. Which of the bounded regions is meant?

    (The parabola is not tangent to the circle!)
    Attached Thumbnails Attached Thumbnails Volume integral set-up-par_und_kreis.png  
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  5. #5
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    There is no additional specification, but I believe it is referring to the area between the circle and the parabola in Quadrants I and IV (i.e. positive x) So the big area between the parabola and circle in the positive x side, as well as the small areas on the top and bottom in the picture.
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  6. #6
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    And actually I think the picture is not completely correct. It as given as x=sqrt(4-y^2), not x^2+y^2=4, and so, it should only be half a circle (the right half), no?
    Last edited by twittytwitter; February 10th 2010 at 10:40 AM.
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