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

Question

zepelin [54]

3 years ago

14

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.

Mathematics

2 answers:

vodomira [7]3 years ago

4 0

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

Tresset [83] · Answer 1 · 2022-06-10T12:16:05+03:00

Tresset [83]3 years ago

3 0

Answer:

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Step-by-step explanation: