# Multiple integration help......

Printable View

• May 26th 2008, 04:05 PM
drala
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 (Headbang).

Any help would be most appreciated.
• May 28th 2008, 01:29 AM
drala
shameless bump
• May 28th 2008, 03:45 AM
Moo
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,

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

...

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