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.