Question

$\int_{y=1}^3\int_{x=0}^{3}$ (1 + 8xy) dx dy

Answer 1

$$\displaystyle\int_{y=1}^3\displaystyle\int_{x=0}^3(1+8xy)dxdy$$

$$=\displaystyle\int_{y=1}^3\big[x+4x^2y\big]\begin{matrix} 3 \\ 0 \end{matrix}dy$$

$$=\displaystyle\int_{y=1}^3(3+36y)dy$$

$$=\big[3y+18y^2\big]\begin{matrix} 3 \\ 1 \end{matrix}$$

$$=9+162-3-18=150$$