- #1

- 82

- 0

## Homework Statement

Evaluate by changing to spherical coordinates

[tex]\int^1_0\int^{\sqrt{1-x^2}}_0\int^{\sqrt{2-x^{2}-y^2}}_{\sqrt{x^{2}+y^2}}xydzdydx[/tex]

## Homework Equations

[tex]dz dy dz = {\rho}^{2}sin{\phi}[/tex]

## The Attempt at a Solution

This problem is quite simple to do in cylindrical coordinates, which I believe gives 0 because of a [tex]sin{\theta}cos{\theta}[/tex] term being integrated from 0 to 2pi, but the request is to use spherical coordinates. The bounds on the integral make a cylinder with radius 1 sandwiched between two cones. Since those bounds obviously don't have spherical symmetry, I am lost as to how to make the conversion.