1. Section 8.7 Improper Integrals I
MAT 1235 Calculus II
Section 8.7
Improper Integrals I

2. HW
WebAssign 8.7 Part I

3. Basic Idea

4. Probability & Statistics

5. Other Applications
Laplace Transform to solve Differential Equations (MAT 3237)
Physics (QM)

6. Preview Two types of Improper Integrals
Infinite Intervals
Discontinuous Integrands
𝑝-integrals (Use in section 8.7 Part II, Calculus III)
Comparison Theorem

7. Preview Two types of Improper Integrals
Infinite Intervals
Discontinuous Integrands
𝑝-integrals (Use in section 8.7 Part II, Calculus III)
Comparison Theorem

8. Fundamental Theorem of Calculus Part 1

9. Fundamental Theorem of Calculus Part 1

10. Type I

11. Improper Integral of Type I
The integral is convergent if the limit exists.
Otherwise, it is divergent.

12. Example 1

13. Remarks
Must have the limit notations
Can be divide into 2 steps

14. Example 2

15. Remarks

16. 𝒑-integrals (Standard Result)
Use in 8.7 Part II (Comparison Theorem)
Calculus III

17. Example 3

18. Improper Integral of Type I

19. Example 4

20. Example 4