Question

Integrate f(x,y,z)=20xz over the region in the first octant (x,y,z≥0) above the parabolic cylinder z=y2 and below the paraboloid z=8−2x2−y2.

Answer 1

$\displaystyle\iiint_Vf(x,y,z)\,\mathrm dV=20\int_{x=0}^{x=2}\int_{y=0}^{y=2}\int_{z=y^2}^{z=8-2x^2-y^2} xz\,\mathrm dz\,\mathrm dy\,\mathrm dx=\dfrac{1280}3$

Answer 2

Answer:

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