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# 14.6 Triple Integrals PowerPoint PPT Presentation

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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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.

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

### Example 1

Evaluate the triple iterated integral

### Example 2

Find the volume of the ellipsoid given by

### Example 3

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