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,

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

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

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

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

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

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

Any help would be most appreciated.

shameless bump

Hello,

Quote:

Originally Posted by drala

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,

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

...

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