Answer
(a) $2+8y^2$
(b) $3x(1+9x)$
Work Step by Step
$f(x,y) = x + 3x^2 y^2$
(a) $ \int_0^2 f(x,y) dx = \int_0^2 (x + 3x^2 y^2) dx$
$= (\frac{x^2}{2} + x^3 y^2)\big|_0^2$
$= [(2+8y^2)-(0)]$
$= 2+8y^2$
(b) $ \int_0^3 f(x,y) dx = \int_0^3 (x + 3x^2 y^2) dy$
$= (xy + x^2 y^3)\big|_0^3$
$= [(3x+27x^2)-(0)]$
$= 3x(1+9x)$
