notes Overview of Improper Integrals

Thomas' Calculus: Early Transcendentals

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Overview of Improper Integrals MAT 104 Frank Swenton, Summer 2000 Definitions A proper integral is a definite integral where the interval is finite and the integrand is defined and continuous at all points in the interval. Proper integrals always converge, that is, always give a finite area The trouble spots of a definite integral are the points in the interval of integration that make it an improper integral, i.e., keep it from being proper. They are of two types: a. Points where the integrand is undefined or discontinuous b. and- are always trouble spots when they appear as limits of integration A simple improper integral is an improper integral with only one trouble spot, that trouble spot being at an endpoint of the interval. Simple improper integrals are defined to be the appropriate limits of proper integrals, e.g.: Z 1 1 x dx = lim + Z 1 1 x dx If the limit exists as a real number, then the simple improper integral is called convergent . If the limit doesnt exist as a real number, the simple improper integral is called divergent . Dealing with improper integrals First step: always locate all trouble spots and split the integral into simple improper integrals, then deal with the pieces individually.deal with the pieces individually....
View Full Document

This note was uploaded on 02/12/2008 for the course MATH 104 taught by Professor Nelson during the Fall '07 term at Princeton.

Page1 / 2

notes Overview of Improper Integrals - Overview of Improper...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online