1. Improper Integrals
Lesson 8.8

2. Improper Integrals Note the graph of y = x -2
We seek the area under the curve to the right of x = 1
Thus the integral is
Known as an improper integral

3. To Infinity and Beyond
To solve we write as a limit (if the limit exists)

4. Evaluate the integral using b
Improper Integrals
Evaluating
Take the integral
Evaluate the integral using b
Apply the limit

5. To Limit Or Not to Limit The limit may not exist Consider
Rewrite as a limit and evaluate

6. To Converge Or Not For A limit exists (the proper integral converges)
for p >1
The integral diverges
for p ≤ 1

7. Improper Integral to -
Try this one
Rewrite as a limit, integrate

8. When f(x) Unbounded at x = c
When vertical asymptote exists at x = c
Given
As before, set a limit and evaluate
In this case the limit is unbounded

9. Using L'Hopital's Rule Consider Start with integration by parts
dv = e –x and u = (1 – x)
Now apply the definition of an improper integral

10. Using L'Hopital's Rule We have
Now use L'Hopital's rule for the first term

11. Assignment
Lesson 8.8
Page 585
Exercises 1 – 45 EOO