How would you write down an integral for the volume of the section of a solid sphere x^2+y^2+z^z

Question

How would you write down an integral for the volume of the section of a solid sphere x^2+y^2+z^z<=2 that lies in the first octant and above the plane z=1 in cylindrical coordinates? I know that x=rcosTHETA, y=rsinTHETA and z=z and how to set up a general integral, but not a bounded one...

anonymous · Answer

I also know that dV=rdzdrdTHETA

anonymous · Answer

So far I have z bounded as 0(lowerbound) and sqrt(2-r^2)(upperbound), THETA 0(lowerbound) and .5pi(upperbound) and r as 1(lowerbound) and sqrt(2)(upperbound)

Please help! I'm really trying to solve this and not wait for an answer!

anonymous · Answer

*waiting