𝑥 2 + 𝑦 2 𝑑𝐴; 𝑅 ={ ( 𝑥, 𝑦 ) | −1 ≤ 𝑥 ≤ 1, 0 ≤ 𝑦 ≤ 2 }

That means $\displaystyle\int^{2}_{0}\int^{1}_{-1}x^2+y^2 dx dy$

$\displaystyle\int^{2}_{0}\int^{1}_{-1}x^2+y^2 dx dy\\ =\displaystyle\int^{2}_{0}\left[\dfrac{x^3}{3}+xy^2\right]^{1}_{-1}dy\\ =\displaystyle\int^{2}_{0}\left(\dfrac{2}{3}+2y^2\right)dy\\ =\left[\dfrac{2y}{3}+\dfrac{2y^3}{3}\right]^{2}_{0}\\ =\dfrac{20}{3}$