Answer to Question #216927 in Calculus for Gayathri Pranathi

Question

Find the volume of the cube bounded by the coordinate planes and the planes X=2 y=2 and z=2 in the first octant

Answer 1

$$V=\displaystyle\int_{0}^{2}\displaystyle\int_{0}^{2}\displaystyle\int_{0}^{2}dzdydx$$

$$=\displaystyle\int_{0}^{2}\displaystyle\int_{0}^{2}[z]\begin{matrix} 2\\ 0 \end{matrix}dydx$$

$$=2\displaystyle\int_{0}^{2}\displaystyle\int_{0}^{2}dydx$$

$$=2\displaystyle\int_{0}^{2}[y]\begin{matrix} 2 \\ 0 \end{matrix}dx$$

$$=4[x]\begin{matrix} 2 \\ 0 \end{matrix}$$

$$=8 (units^3)$$

$V=8\ cubic\ units$