Answer
7/6
Work Step by Step
First, expand $$(x+y)^2$$ to get
$$\int_{0}^{1}\int_{0}^{1} (x^2+2xy+y^2)dxdy$$
Then integrate with respect to x
$$\int_{0}^{1}\int_{0}^{1} (x^2+2xy+y^2)dxdy$$=$$\int_{0}^{1} [(\frac{x^3}{3}+x^2y+xy^2)]_{0}^{1}dy$$
Lastly, integrate with respect to y.
$$\int_{0}^{1}(1/3+y+y^2)dy$$
=$$[\frac{y}{3}+\frac{y^2}{2}+\frac{y^3}{3}]_{0}^{1}$$
=$$\frac{1}{3}+\frac{1}{2}+\frac{1}{3}$$
=$$\frac{7}{6}$$
