calcular integral com variavel xy

[Bruno27]

Calcular ∫∫f(x,y)dxdy,onde :

f(x,y)=ye⋀xy
onde R é o retângulo 0≤x≤3 e 0≤y≤1

[Sobolev]

\(\int_0^3 \left( \int_0^1 y e^{xy} dy \right) dx = \int_0^1 \left( \int_0^3 y e^{xy} dx \right) dy = \int_0^1 \left[e^{xy}\right]_{x=0}^{x=3} dy = \int_0^1(e^{3y} -1) dy = \cdots\)