God does not care about our mathematical difficulties -he integrates empirically. Summary: Chapter 5 Integrals God does not care about our mathematical difficulties - he integrates empirically. ­Albert Einstein This is a tricky domain because, unlike simple arithmetic, to solve a calculus problem - and in particular to perform integration - you have to be smart about which integration technique should be used: integration by partial fractions, integration by parts, and so on. ­ Marvin Minsky If one looks at the different problems of the integral calculus which arise naturally when one wishes to go deep into the different parts of physics, it is impossible not to be struck by the analogies existing. ­ Henri Poincare As we've seen in the last two chapters, the derivative of f(x) is the rate at which f(x) is changing. In this chapter we will turn this around and learn to deal with the situation where f(x) is the rate at which something is changing. Our goal is to learn to total up that thing and find how much of it there is. Example 5.1 Constant rates of change Suppose that you have a rental property that yields \$1200.00 per month of income but which costs \$560.00 to pay for maintenance, upkeep, insurance, and utilities. Then the rate at which your money-in-hand is changing Collections: Mathematics