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Math Help - Linear Transformation

  1. #1
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    Linear Transformation

    Hey there I need some help with this problem

    Let be the region 0 <(or equal to) y <(or equal to) x
    0 <(or equal to) x <(or equal to) 1

    Evaluate
    double integral over D of (x+y) dxdy

    by making the change of variables x=u+v, and y=u-v

    Check your answers by evaluating the iterated integral directly by using an iterated integral.


    Please explain each step you did, so I can understand how to do this problem thanks.
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  2. #2
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    Re: Linear Transformation

    Hey gfbrd.

    Its better that you show us your attempt rather than us do it for you. First try using the substitution formula and calculating the Jacobian and post it in this thread.
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  3. #3
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    Re: Linear Transformation

    Yea sorry I have already calculated the Jacobian which is 2, I just dont know how to find the new limits of integration
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  4. #4
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    Re: Linear Transformation

    As a start, x + y = u + v + (u - v) = 2u. Now find the limits in terms of u and v for x = 0 to 1 and y = 0 to x.

    Also consider when you make a change of the order of integration (as this may explain why they want to use the new parameterization in terms of u and v).
    Thanks from gfbrd
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  5. #5
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    Re: Linear Transformation

    Alright I figured it out thanks for your help
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