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    trying to integrate x^2 + y^2 dx dy over the region bounded by y=x, y=x+2, y=-x, and y=-x+2

    so im changing variable using u=x+y v=x-y, but using change of variable i get the answer to be -8/3, whereas computing it straight i get 8/3...not sure what's going wrong? Which is the right answer?

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    The Jacobian is negative - are you taking the modulus of it?
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    ??
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    Err, yes, you do, mandaben / King of TSR. :curious:
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    (Original post by King of TSR)
    I thought it was just the determinant of the matrix thing rather than the modulus - is that not what the lines mean in this context?

    or is the jacobian always positive?
    The Jacobian, denoted J, is defined to be a determinant, not a matrix. So |J| means the absolute value of the determinant.
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    haha okay!
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    hijacked
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    http://en.wikipedia.org/wiki/Jacobia...nd_determinant

    in the example here the jacobian is negative?
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    ahh i see now..

    delete?
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    (Original post by mandaben)
    http://en.wikipedia.org/wiki/Jacobia...nd_determinant

    in the example here the jacobian is negative?
    Yeah, but in the example (under Jacobian determinant) they're merely computing the determinant and not doing actually utilizing it. Whereas the substitution rule specifically requires the absolute value of the determinant.
 
 
 

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