7.6 Improper Integrals Tues Jan 19 Do Now Evaluate

HW Review

Improper Integrals Areas of unbounded are represented by improper integrals An integral is improper if – The interval of integration may be infinite (bound to infinity) – The integrand may tend to infinity (vertical asymptote in the bounds)

Improper integral Assume f(x) is integrable over [a,b] for all b>a. The improper integral of f(x) is defined as The improper integral converges if the limit exists (and is finite) and diverges if the limit does not exist

Ex Evaluate

Ex Determine whetherconverges or not

The p-integral For a > 0, if P > 1 The integral diverges if P <= 1

Ex Evaluate

Comparing Integrals Sometimes we are interested in determining whether an improper integral converges, even if we cannot find its exact value. If we can compare the integral to one we can evaluate, we can determine if it converges or not

Comparison Test Assume thatand a >=0 Ifconverges, then also converges If diverges, thenalso diverges

Ex Show thatconverges

Ex Doesconverge?

Ex Doesconverge?

Closure Evaluate if possible HW: p.444 #