1. 14.6 Triple Integrals
Seventeenth-Century French mathematician Pierre de Fermat wrote in the margin of his copy of Arithmetica by Diophantus, near the section on the Pythagorean Theorem (a squared plus b squared equals c squared), "x ^ n + y ^ n = z ^ n - it cannot be solved with non-zero integers x, y, z for any exponent n greater than 2. I have found a truly marvelous proof, which this margin is too small to contain." This was left as an enigmatic riddle after Fermat's death and it became a famous, unsolved problem of number theory for over 350 years.
Andrew Hanson has made some pictures, and I have in turn made sculpture, of a system analogous to Fermat's last theorem - a superquadric surface parameterized complex four-space.
Taken from:

2. Recall
Find the area of the region by using the integration order dy dx

3. Example 5 Solution 2

4. Example 1
Evaluate the triple iterated integral

5. Solution Example 1

8. Example 2
Find the volume of the ellipsoid given by

9. Solution Example 2

10. Example 3
Evaluate the given integral (Hint: change the order of integration)

11. Example 3 solution

13. Figure 14.52

14. Figure 14.59