MATH 2B Chapter Notes - Chapter 7.8: Ultraviolet Divergence, Improper Integral, 4Dx

• School: UC-Irvine
• Department: Mathematics
• Course: MATH 2B
• Professor: George Donaldson

Document Summary

The riemann sum de nition of an integral has problems if the endpoints a, b are in nite or if f is unde ned at x = a or x = b. Type 1 a = and/or b = : we writer b. Type 2 f is discontinuous at x = a and/or b. F (x) dx orr a f (x) dx. a f (x) dx is improper in either of the following cases: y. An integral could be type 1 at one end and type 2 at the other, e. g. z . Just because we can write down an integral does not mean that it exists! The existence or otherwise of improper integrals relies on the existence of certain limits. For our example of a type i integral above, it is clear that for any nite value t, we have t. It seems reasonable that ifr t z t.