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

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- May 25th 2010, 01:26 PMmike21double integrals
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 25th 2010, 01:37 PMGeoC
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 25th 2010, 02:05 PMGeoC
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)