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Thread: Multiple integration help......

  1. #1
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    Multiple integration help......

    Hi folks,

    I am having a hard timne getting my head around a problem involving double integrals, was hoping someone more learned the myself could nudge me in the right direction.

    ok, suppose we have,

    $\displaystyle p=5A^3$,
    $\displaystyle A = xy$,
    $\displaystyle dA = dxdy$

    Now, define $\displaystyle q$ as
    $\displaystyle q =\int p dA $
    $\displaystyle q =\int5A^3 dA $

    Now, in simple terms this is just $\displaystyle \frac{5}{4}A^4$

    Its when I substitute $\displaystyle A$ for $\displaystyle xy$ that i get problems...

    $\displaystyle q =\int\int 5x^3 y^3 dxdy $
    $\displaystyle q =\int \frac{5}{4} x^3 y^4 dx $
    $\displaystyle q =\frac{5}{16} x^4 y^4$
    $\displaystyle q =\frac{1}{4} \frac{5}{4} A^4$

    I can see that the this extra factor $\displaystyle \frac{1}{4}$ comes from integrating twice.... but i dont understand why it comes about .


    Any help would be most appreciated.
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  3. #3
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    Hello,

    Quote Originally Posted by drala View Post
    Hi folks,

    I am having a hard timne getting my head around a problem involving double integrals, was hoping someone more learned the myself could nudge me in the right direction.

    ok, suppose we have,

    $\displaystyle p=5A^3$,
    $\displaystyle A = xy$,
    $\displaystyle {\color{red}dA = dxdy}$

    ...
    It's because this line is not correct... the product rule doesn't say that the derivative of xy is dxdy
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