MTH 251 Study Guide - Midterm Guide: Farad
Document Summary
Section 7. 8: improper integrals (continue) are called convergent if their respective i. ii. provided this limit exists. Definition of improper integrals of type 1(the interval is infinite): exists for every t , then we can define () = lim () If () limits exist, and divergent if their limits do not exist. iii. Example exists for every t b, then we define () = and () both exist then we define () 4+4 use u substitution where u=2, du=2zdz, and 12 =, so. For what values of p does 1. = lim || 1 and the lim || = , so p=1 does not work. 1 1 0 as t , and thus lim 11 (1 1) = 1 1 and so it converges. Final statement: the integral 1 converges for p> 1 and diverges for p 1. Definition of improper integrals type 2(when the interval is not infinite)
