Evaluate the triple integral ∭EzdV where E is the solid bounded by the cylinder y2+z2=81 and the planes x=0,y=9x and z=0 in the first octant.

I = 91.125

Step-by-step explanation:

Given that:

where E is bounded by the cylinder and the planes x = 0 , y = 9x and z = 0 in the first octant.

The initial activity to carry out is to determine the limits of the region

since curve z = 0 and

∴

Thus, z lies between 0 to

GIven curve x = 0 and y = 9x

As such,x lies between 0 to

Given curve x = 0 , and z = 0,

y = 0 and

∴ y lies between 0 and 9

Then

I = 91.125

the answer will be