Understanding Integration Limits for Spherical and Cartesian Coordinates

[MoAli]

Homework Statement

Shown in the photo attached.

2. Homework Equations
∫_V r²Sinθdθdφdr in spherical coordinates
∫_V dxdydz in cartesian coordinates
equation of a sphere x²+y²+z²=r²

The Attempt at a Solution

In this case y=(y-2): sphere displaced on the y-axis. and since it is bound by all planes its going to be one quarter of a sphere. I don't get the part where the question says translate the origin to the shape centre, how can I do this? and also I need someone to check my limits of integration. I attached my answer.

 

[BvU]

Hi,

Can't say I understand your integration limits for the second part. Care to explain ? And where does the factor 2 come from ?