Hi,(adsbygoogle = window.adsbygoogle || []).push({});

I'm having a trouble doing this:

Compute volume of the solid

[tex]

T = \left\{[x,y,z] \in \mathbb{R}^3; x \geq 0, y \geq 0, 0 \leq z \leq 1 - x - y\right\}

[/tex]

First I need to express bounds for [itex]x[/itex] and [itex]y[/itex], for [itex]z[/itex] I have it already. So because

[tex]

0 \leq z \leq 1 - x - y

[/tex]

then

[tex]

0 \leq x \leq 1 - z - y

[/tex]

and also

[tex]

0 \leq y \leq 1 - z - x

[/tex]

But that's probably not the right approach, because evaluating integral

[tex]

\iiint_{T}\ dx\ dy\ dz = \int_{0}^{1-z-x}\int_{0}^{1-z-y}\int_{0}^{1-x-y}\ dz\ dx\ dy

[/tex]

still lefts me with some [itex]z[/itex] and [itex]x[/itex] variables at the end...

Will somebody point me to the right direction?

Thank you.

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# Homework Help: Yet another volume

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