Question

If fie=2x+2, evaluate volume integral where R is the region of the cube bounded by the plane x=0 ,x=1, y=0, y=1 ,z=0, z=1

Answer 1

$$\displaystyle\int_{0}^1\displaystyle\int_{0}^1\displaystyle\int_{0}^1(2x+2)dzdxdy$$

$$=\displaystyle\int_{0}^1\displaystyle\int_{0}^1(2x+2)dxdy$$

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

$$=\displaystyle\int_{0}^13dy=3$$