Double Integral Volume

Double Integral Version

• Suppose $R$ is a Region in ${\mathbb{R}}^2$
• Suppose $f:R\to \mathbb{R}$ is a non-negative function with $f(x,y)\ge 0$
• The volume above $R$ and below $f$ is:

$$\int {\int }_{R}f(x,y)dA=\int {\int }_{R}f(x,y)dxdy$$

Note that:

• $dA$ is an Area Element of $dxdy$ and $dydx$