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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 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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  1. 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.

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

  3. Example 5 Solution 2

  4. Example 1 Evaluate the triple iterated integral

  5. Solution Example 1

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

  7. Solution Example 2

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

  9. Example 3 solution

  10. Figure 14.52

  11. Figure 14.59

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