1. 7.6 Improper Integrals Tues Jan 19 Do Now Evaluate

2. HW Review

3. 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)

4. 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

5. Ex Evaluate

6. Ex Determine whetherconverges or not

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

8. Ex Evaluate

9. 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

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

11. Ex Show thatconverges

12. Ex Doesconverge?

13. Ex Doesconverge?

14. Closure Evaluate if possible HW: p.444 #11 15 21 25 27 35 37 44 47 53 56 63 71 81