Question

Resolva as integrais ∫∫(xy³dydx

Answer 1

$\int\int xy^3\,dydx~=~\int\left(\int\,xy^3dy\right)dx\\\\\\Para~a~integral~em~relacao~a~dy~"x"~\acute{e}~cte\\\\\\\int\left(\int\,xy^3dy\right)dx~=~\int\left(x\,.\,\frac{y^4}{4}\right)dx\\\\\\Para~a~integral~em~relacao~a~dx~"y"~\acute{e}~cte\\\\\\\int\left(x\,.\,\frac{y^4}{4}\right)dx~=~\frac{x^2}{2}~.~\frac{y^4}{4}~+~K~=~\boxed{\frac{x^2y^4}{8}+k}$