Is my calc. for triple integral correct? int[B]x^2y^2z^2 dV = 1/5, B={0 <=x<=y<=z<=1}
So I'm asked to calculate the triple integral
\(\displaystyle \iiint_{B} x^2 y^2 z^2 dV\) for a region B defined as 0 <=x<=y<=z<=1.
My setup is therefore
\(\displaystyle \int[0,1]\int[0,z]\int[0,y] x^2 y^2 z^2 dxdydz\). I then went on to evaluate this, and got 1/5. Is this correct?
So I'm asked to calculate the triple integral
\(\displaystyle \iiint_{B} x^2 y^2 z^2 dV\) for a region B defined as 0 <=x<=y<=z<=1.
My setup is therefore
\(\displaystyle \int[0,1]\int[0,z]\int[0,y] x^2 y^2 z^2 dxdydz\). I then went on to evaluate this, and got 1/5. Is this correct?
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