Multiple integral

[nicoc]

Hello,

I would appreciate if someone can help me to calculate the volume of the domain in the picture.

 

[Steven G]

Sure, what do you need help with?

 

[nicoc]

First, As I don't have to integrate any function, just integrating f(x)=1 on D is enough right?

I know the first part of the domain is a sphere of radius r, what I cant understand is the second part?

 

[Dr.Peterson]

I'd start by plotting x^2 + y^2 = |rx| on a plane. Since the second inequality has no z, it represents a cylinder with this curve as its base.

Once you've done that, you can decide whether to integrate (yes, if you do a triple integral the integrand will be 1) in rectangular coordinates or some other. Then choose the order of integration and set up limits.

If you are having trouble plotting that curve, show us how far you got, and what is stopping you.