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**Ant** I'm trying to compute the area of the Cone (Z = sqrt[ x^2 + y^2] below the plane z = 2.

Using cylindricl polars coordinates:

phi: [ -pi/2, pi/2]

r: [ 0, 2]

z: [ r, 2]

with the Jacobian being r.

I get 4/3 pi which I think is the correct answer.

However, using Spherical polar coordinates and using the following limits:

Phi: [ -pi/2, pi/2 ]

Theta: [ 0, pi/4 ]

r: [ 0, 2 ]

with the Jacobian being r^2 sin (theta) I'm getting a different answer. Could anyone tell me if my limits are correct?

Thanks!