Evaluate the triple integral ∭z dxdydz where E is the solid bounded by the cylinder y^2+z^2=81 and the planes x=0,y=9x and z=0 in the first octant.

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Evaluatethetripleintegral∭zdxdydzwhereEisthesolidboundedbythecylindery^2+z^2=81andtheplanesx=0

Evaluate the triple integral ∭z dxdydz where E is the solid bounded by the cylinder y^2+z^2=81 and the planes x=0,y=9x and z=0 in the first octant.
Evaluate the triple integral ∭z dxdydz where E is the solid bounded by the cylinder y^2+z^2=81 and the planes x=0,y=9x and z=0 in the first octant.

Evaluate the triple integral ∭z dxdydz where E is the solid bounded by the cylinder y^2+z^2=81 and the planes x=0,y=9x and z=0 in the first octant.
∫∫∫z dxdydz=∫(1→0) dx ∫(9→9x) dy ∫(√(81-y^2)→0) zdz
=∫(1→0) dx ∫(9→9x) (81-y^2)/2 dy
=∫(1→0) (243-729x/2+243x^3/2) dx
=729/8

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