Answer to Question #197456 in Calculus for Fatima

Question

Evaluate the iterated Integral  in terms of e. 

Answer 1

For example:

$\displaystyle \iint_Re^{xy}dA,\ R=[2,4]\times [1,2]$

Then:

$\displaystyle \iint_Re^{xy}dA=\displaystyle\int^4_2\int^2_1e^{xy}dydx=\displaystyle\int^4_2(e^{xy}|^2_1)dx=$

$\displaystyle\int^4_2(e^{2x}-e^x)dx=(e^{2x}/2-e^x)|^4_2=e^8/2-e^4-e^4/2+e^2=e^8/2-3e^4/2+e^2$