- #1

- 23

- 0

_{0}

^{3}∫

_{0}

^{sqrt(9-x2)}∫

_{sqrt(x2+y2)}

^{sqrt(18-x2-y2)}(x

^{2}+y

^{2}+z

_{2})dzdxdy

x=[itex]\rho[/itex]sin[itex]\varphi[/itex]cosθ

y=[itex]\rho[/itex]sin[itex]\varphi[/itex]sinθ

z=[itex]\rho[/itex]cos[itex]\varphi[/itex]

Change the integrand to [itex]\rho[/itex] and integrate wrt d[itex]\rho[/itex]dθd[itex]\varphi[/itex]

I don't know how to find the limits of integration. Normally I would draw a picture and reason it out, but that doesn't seem plausible here.

Thanks.