(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Rewrite this integral the other five ways

[tex]\int_{x=0}^{1}\int_{z=0}^{1-x^2}\int_{y= 0}^{1-x} dydzdx[/tex]

2. Relevant equations

Must be in rectangular coordinates

3. The attempt at a solution

1.)[tex]\int_{z=0}^{1}\int_{x=0}^{\sqrt{1-z}}\int_{y= 0}^{1-x} dydxdz[/tex]

2.)[tex]\int_{x=0}^{1}\int_{y=0}^{1-x}\int_{z=0}^{1-x^2}dzdydx[/tex]

3.)[tex]\int_{y=0}^{1}\int_{x=0}^{1-y}\int_{z=0}^{1-x^2}dzdxdy[/tex]

4.)[tex]\int_{z=0}^{1}\int_{y=0}^{1-x}\int_{x=0}^{\sqrt{1-z}}dxdydz[/tex]

5.)[tex]\int_{y=0}^{1}\int_{z=0}^{1-x^2}\int_{x= 0}^{1-y}dxdzdy[/tex]

With the last two I see the problem that the variable x will still be in the final answer. How can this problem be fixed. I figured the solution is to write the planes in another form but I don't see how to write the equations y=1/x or z=1-x^{2}without the variable x.

Thank you for your time.

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# Homework Help: Rewriting triple integrals

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