1. Improper Integrals (8.8) Tedmond Kou Corey Young

2. Overview There are two types of improper integrals: 1) A definite integral with limits to infinity.

3. Overview 2 2) A definite integral that contains a discontinuity within its limits. Discontinuity at point c c c = +

4. Tips and Tricks 1) Graph the function so that you know what it looks like. Example: f(x)=xe -x 2

5. Tips and Tricks 2 2) Identify the kind of function, then utilize specific integration techniques. Integration by Parts Trig Substitutions Partial Fractions u du substitution Split limit into two xe -x 2 dx

6. Basic Steps 1) Identify the type of improper integral. xe -x 2 dx Split into two and each one becomes a definite integral with limits to infinity

7. Basic Steps 2/3 2) Take the limit to the point of infinity or discontinuity. 3) Take the anti-derivative

8. Basic Step 4 4) Plug in the numbers to check if the function is convergent or divergent.

9. Comparative Theorem

10. Examples with walkthrough Definite integral with limits to infinity:

11. Diverges

12. Examples with walkthrough Definite integral with discontinuous integrand:

13. Examples with walkthrough Comparative Theorem: Determine if the following integral is convergent or divergent.