Answer
$500y^{3},\qquad 3x^{2}$
Work Step by Step
Working on $\displaystyle \int f(x,y)dx$, treat y as a constant.
$\displaystyle \int_{0}^{5}12x^{2}y^{3}dx =12y^{3}\displaystyle \int_{0}^{5}x^{2}dx$
$=12y^{3}[\displaystyle \frac{x^{3}}{3}]_{x=0}^{x=5}$
$=4y^{3}[5^{3}-0^{3}]$
$=500y^{3}$,
Working on $\displaystyle \int f(x,y)dy$, treat $x$ as a constant.
$\displaystyle \int_{0}^{1}12x^{2}y^{3}dy =12x^{2}\displaystyle \int_{0}^{1}y^{3}dy$
$=12x^{2}[\displaystyle \frac{y^{4}}{4}]_{y=0}^{y=1}$
$=3x^{2}[1^{4}-0^{4}]$
$=3x^{2}$
