- #1

jj2443

- 10

- 0

## Homework Statement

Compute the centroid of the region defined by x[itex]^{2}[/itex] + y[itex]^{2}[/itex] + z[itex]^{2}[/itex] [itex]\leq[/itex] k[itex]^{2}[/itex] and x [itex]\geq[/itex] 0 with [itex]\delta[/itex](x,y,z) = 1.

## Homework Equations

[itex]\overline{x}[/itex]=[itex]\frac{1}{m}[/itex][itex]\int[/itex][itex]\int[/itex][itex]\int[/itex] x [itex]\delta[/itex](x,y,z) dV

[itex]\overline{y}[/itex]=[itex]\frac{1}{m}[/itex][itex]\int[/itex][itex]\int[/itex][itex]\int[/itex] y [itex]\delta[/itex](x,y,z) dV

[itex]\overline{z}[/itex]=[itex]\frac{1}{m}[/itex][itex]\int[/itex][itex]\int[/itex][itex]\int[/itex] z [itex]\delta[/itex](x,y,z) dV

## The Attempt at a Solution

I understand that I need to integrate each of the above equations to get the x,y,z coordinates of the centroid, but how do I determine the bounds of integration?

Any help would be much appreciated! Thanks!