Chapter 14, Problem 1GYR

To determine

Provide notes on the double integral of a function of two variables over a region in the coordinate plane.

Explanation of Solution

The double integral of a function of two variables $f\left(x,y\right)$ over a region in the coordinate plane as the limit of approximating Riemann sums.

When a limit of the sums $S_n$ exists, giving the same limiting value, then the function f is said to be integrable and the limit is known as double integral of f over the region R. It can be written as,

${\displaystyle \underset{R}{\iint }f\left(x,y\right)dA}$ or ${\displaystyle \underset{R}{\iint }f\left(x,y\right)dxdy}$