Calculus solves two main problems. The first problem is measuring how fast quantities change. This is solved by diiffferential calculus through the concept of the derivative of a function. The second problem is measuring things that can be approximated as sums of many small pieces; its solution constitutes integral calculus. Integral calculus solves many seemingly unrelated problems of computing: area, volume, work, and pressure on a dam are examples. The most striking thing of all in calculus is that the two problems are closely related; each problem is the “inverse” of the other!
KeywordsShade Region Trapezoidal Rule Fundamental Theorem Numerical Integration Method Mean Value Theorem
Unable to display preview. Download preview PDF.