Final answer:
To calculate the double integral of a function over a region, set up and evaluate the integral twice, once for each variable. This is commonly used in fields like physics to find work or flux.
Step-by-step explanation:
The student asked how to calculate the double integral of a scalar function f(x,y) over a region D in the two-dimensional xy plane. Since the integration is over an area, the procedure involves setting up the double integral with the limits of integration corresponding to the bounds of region D. To solve this, one must perform the integration twice, once for each variable, by finding the antiderivative with respect to one variable and then evaluating it over the interval determined by the other variable. This concept is often applied in physics and engineering to calculate quantities like work or flux over a certain region.