Chapter 5 details just what a double integral is, and shows how it can be evaluated in terms of iterated single integrals. Chapter 6 makes use of the double integral to calculate area of a plane region, volume under a surface, the surface area of a surface, and the average value of a function of two independent variables.
In addition, the double integral is used to compute the first moments of a plane region, and from these moments, the centroid (geometric center) of the region or the center of mass of a plane lamina occupying that region. The double integral is also used to calculate the second moments of a plane region about the coordinate axes, from which the moments of inertia about these axes is obtained.
