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
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.
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Recall
Find the area of the region by using the integration order dy dx
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Example 5 Solution 2
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Example 1
Evaluate the triple iterated integral
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Solution Example 1
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Example 2
Find the volume of the ellipsoid given by
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Solution Example 2
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Example 3Evaluate the given integral (Hint: change the
order of integration)
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Example 3 solution
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Figure 14.52
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Figure 14.59