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Math Help - Double or Triple integration (Find the area ) Uncommon question

  1. #1
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    Double or Triple integration (Find the area ) Uncommon question

    The question is:
    Double or Triple integration (Find the area ) Uncommon question-integration_area.png
    Please click the picture above.
    I let x^2+y^2=a^2 be the vertical cylinder, and I tried to find
    1)the intersections between x^2+y^2=a^2 and z=2xy
    2)the intersections between x^2+y^2=a^2 and z=x^2+y^2
    and then don't know how to do.
    I need to show the two area is the same, but i don't know how to show.
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  2. #2
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    Re: Double or Triple integration (Find the area ) Uncommon question

    Hey happymatthematics.

    What did you get for the intersections? (Once you have these then they become the limits for your area integral).
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  3. #3
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    Re: Double or Triple integration (Find the area ) Uncommon question

    hello chiro,
    the following is my attempt.
    Double or Triple integration (Find the area ) Uncommon question-vertical_cylinder_area.png

    I found them in parametric form.
    I now have three variables, including x, y, z, but I learnt to find area by double integration. so how to find area of three variables?
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  4. #4
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    Re: Double or Triple integration (Find the area ) Uncommon question

    What are your limits of integration? You will be integrating over a region with specific limits.

    Once you show the limits (and how you derived them), then we can take it from there.
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