Double Integrals

The double integral is the analogue of the single integral (definite integral) suggested by Figure 12.1.1. Figure 12.1.1 (a) shows the area A bounded by the interval [a, b] and the curve y = f(x), and corresponds to the single integral

Figure 12.1.1 (a) Area:

Figure 12.1.1(b) shows the volume V bounded by the plane region D and the surface z = f(x, y), and corresponds to the double integral

Figure 12.1.1(b) Volume:

Our development of double integrals will be similar to our development of single integrals in Chapter 4. Before going into detail, we give a brief intuitive preview.