anonymous
  • anonymous
evaluate triple integrate xzdV, where s is the solid tetrahedron with vertices <0,0,0> <0,1,0> <2,1,0> <2,1,3> someone help
MIT 18.02 Multivariable Calculus, Fall 2007
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
ok, let's draw the tetrahedron first. |dw:1332863302419:dw| Not the best drawing but gives you an idea
anonymous
  • anonymous
Now let's try to figure out what is going on in the x-y plane. |dw:1332863444329:dw| Ok, it looks like we have a type I region where \[0\le x \le 1\] and \[\frac{1}{2}x \le y \le1 \]So, we have:\[\int\limits \int\limits \int\limits_{E}xzdV=\int\limits_{0}^{1}\int\limits_{\frac{1}{2}x}^{1}\int\limits_{h_{1}(x,y)}^{h_{2}(x,y)}xzdzdydx\]Now you just need to find the bounds on the z-coordinate and you're home free :)
anonymous
  • anonymous
made an error in the above...the limits of x are: \[0\le x \le 2\]

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