MATH 141 Study Guide - Comprehensive Final Guide: Improper Integral, Convergent Boundary, Divergent Boundary

• School: McGill University
• Department: Mathematics and Statistics
• Course: MATH 141
• Professor: Axel Hundemer

Document Summary

Definition: the area a of the region s that lies under the graph of a continuous function f is the limit of the sum of the areas of approximating rectangles. Definition of a definite integral: if f is a function defined for , we divide the interval [a,b] into n subintervals of equal width . We let be the endpoints of these subintervals and we let be any sample points in these subintervals, so lies in the ith subinterval . Then the definite integral of f from a to b is: Provided that this limit exists and gives the same value for all possible choices of sample points. If it does exist, we say that f is integrable on [a,b]. Theorem: if f is continuous on [a,b] , or if f only has a finite number of jump discontinuities, then f is integrable on [a,b]. Part 1: if f is continuous on [a,b], then the function g defined by: