Multiple integrals

This chapter highlights multiple integrals. It begins by presenting a couple of physical examples of multiple integrals, including double integrals which can also be called surface integrals. As a concrete example of how to calculate multiple integrals, the chapter considers a very easy case, namely, working out the formula for the area of a right-angled triangle. This illustrates that (for a well-behaved function) the order of integration in a multiple integral does not matter, and that it can be interchanged. The chapter then looks at the choice of coordinates. Multiple integrals, like many other mathematical operations, become much simpler if they are formulated in a coordinate system which matches the geometry of the problem.