1. MAT 1236 Calculus III Section 15.7 Triple Integrals http://myhome.spu.edu/lauw

2. HW WebAssign 15.7 (10 problems, 101 min.)

3. Preview Discuss the definitions of integrals of functions with 3 variables Discuss how the concept is the extension of the 1 and 2-variable case Computing triple integrals

4. 1D Vs 2D Vs 3D

5. Intervals [a,b] Domains

6. (x,f(x)); Curves Graphs

7. Integrals

8. Triple Integral over a Box

9. Geometric Meanings

10. Fubini’s Theorem

11. Splitting Formula

12. Example 1

13. Special Regions

15. Example 2 Find the volume of E, where E is the solid bounded by

16. Expectations You are expected to put down E and D separately.

17. Special Regions

18. Before Next Example... We need to introduce a special type of surface. I added this an hour ago. So it is not on your HO. I usually drew all these pictures by hand. And it may be a good idea to use Maple to illustrate this. Try not to copy too much.

19. Paraboloids One of the most common surfaces They are related to parabolas Projections to the xz- and yz- planes are parabolas

20. Example 3 Find the volume of the solid bounded by the paraboloids

21. Example 3 Find the volume of the solid bounded by the paraboloids

22. Example 3 Find the volume of the solid bounded by the paraboloids

23. Example 3 Find the volume of the solid bounded by the paraboloids

24. Example 3 Find the volume of the solid bounded by the paraboloids

25. Go Nuts! GO NUTS!

26. Go Nuts! Please take one on your way out!