MATH117 Lecture Notes - Lecture 21: Riemann Sum, Farad, Illinois Route 3
19 Oct 2017
School
Department
Course
Professor
Document Summary
Integral calculus is actually much older than di erential calculus. The essential idea is simply that of taking a di cult problem, breaking it down into smaller, more manageable pieces, and then putting the results together ( re-integrating them!). There is one application which is particularly easy to visualize, and so we"ll use that as our motivation. How might we nd the area between its graph and the x-axis, over an interval [a, b]? y=f(x) x=a x=b. You should be able to see numerous ways in which we could nd an approximation; we could split the region up into rectangles and triangles, calculate the area of each one, and add the results. Rather than doing this haphazardly, though, we have a standard algorithm, which will allow us to develop theorems and formulas (and to calculate such an area much more quickly). First, we divide the interval [a, b] into n subintervals of equal length x.
