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

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

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

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

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

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

$=8 (units^3)$

$V=8\ cubic\ units$