Chapter 12, Problem 1PE

To determine

The definition of double integral.

Explanation of Solution

Double integrals are a methods to integrate over a two-dimensional area.

Consider a function of two variables $z=f\left(x,y\right)$ .

The double integral of function $z=f\left(x,y\right)$ is represented by

  $\text{Double Integral}={\displaystyle {\iint }_{R}f\left(x,y\right)dA}$

where R is the region where integration in the xy -plane is done and $dA=dxdy$ .

A double integral is represented as the limit of a Riemann Sum, when integral of a function of one variable is considered.