14 6 triple integrals
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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: http://emsh.calarts.edu/~mathart/sw/Color_3D_Prints.html. 14.6 Triple Integrals.

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14.6 Triple Integrals

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14 6 triple integrals

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 complexfour-space.

Taken from: http://emsh.calarts.edu/~mathart/sw/Color_3D_Prints.html

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.


Recall

Find the area of the region by using the integration order dy dx

Recall


Example 5 solution 2

Example 5 Solution 2


Example 1

Example 1

Evaluate the triple iterated integral


Solution example 1

Solution Example 1


Example 2

Example 2

Find the volume of the ellipsoid given by


Solution example 2

Solution Example 2


Example 3

Example 3

Evaluate the given integral (Hint: change the order of integration)


Example 3 solution

Example 3 solution


Figure 14 52

Figure 14.52


Figure 14 59

Figure 14.59


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