MATH 4389 Study Guide - Final Guide: Improper Integral, Polar Coordinate System, Arc Length

• School: University of Houston
• Department: Mathematics
• Course: MATH 4389
• Professor: Almus

Document Summary

Techniques of integration (integration by parts, partial fraction decomposition ) Finding area under a curve / between two curves. Volume of solid of revolution (disk method, shell method) In the shell method, the rectangle of revolution is parallel to the axis of revolution. Revolving about the y-axis or a vertical axis: Revolving about the x-axis or a horizontal axis: Types of improper integrals: (one or both bounds are infinite) 1 or both bounds are infinite: (infinite discontinuity at a boundary) 5 discontinuity at x = 1: (infinite discontinuity in the interior) 2 is improper because is improper because d x x 1 f x d x x 1. 2 has an infinite discontinuity at x = 1, and 1 is between 2 and 2. B a x d x . f. If f is continuous on b x d x f l i m a. , b , then x d x . f b a.