Answer
$8$
Work Step by Step
Let us suppose that $I=\int_{0}^2 \int_{0}^{1} (1+2x+2y) \ dy \ dx$
Next, we will solve the integral as follows:
$I=\int_{0}^2 [\int_{0}^{1} (1+2x+2y) \ dy] \ dx$
or, $=\int_{0}^2 [(y+2xy+\dfrac{2y^2}{2})]_{0}^{1} \ dx$
or, $=\int_{0}^2 (2x+2) \ dx$
or, $=[2x+\dfrac{2x^2}{2}]_0^2$
or, $=(2)(2)+\dfrac{2(2)^2}{2}$
or, $=8$
