double integrals

Mar 2010
16
0
Having trouble figuring these out.

1. Integral 0 to ln3 integral 0 to ln2 e^x+y dydx

2. Integral 0 to 1 integral 0 to 1 x over (xy+1)^2 dydx
 
May 2010
43
1
Are you asking \(\displaystyle \int_{0}^{ln(3))}e^x dx\int_{0}^{ln(2))}e^ydy\) ?

If so, this is 2*1 = 2....

Remember \(\displaystyle e^{ln(a)} = a\)
 
May 2010
43
1
For second integral, I'm less certain, but here goes:

\(\displaystyle \int_{0}^{1}\int_{0}^{1}\frac{xdxdy}{(1+xy)^2} = \int_{0}^{1}dx\int_{0}^{1}\frac{xdy}{(1+xy)^2}\).

For the integral over y, treat x as a constant, which yields:

\(\displaystyle \int_{0}^{1}\left ( 1-\frac{1}{1+x} \right )dx\)..

Which in turn yields: 1 - ln(2)