Understanding Integration Limits for Spherical and Cartesian Coordinates

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The discussion focuses on understanding integration limits for spherical and Cartesian coordinates in a homework problem involving a sphere displaced along the y-axis. The user expresses confusion about translating the origin to the center of the shape and seeks clarification on their integration limits. They mention that the volume is one quarter of a sphere and ask for help regarding the factor of 2 in their calculations. The conversation highlights the need for a better grasp of coordinate transformations and integration techniques in this context. Overall, the thread emphasizes the complexities of setting up integration limits for different coordinate systems.
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Homework Statement


Shown in the photo attached.
Screen Shot 2017-02-12 at 11.05.57.png


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.
IMG_7777.JPG
 
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Hi,

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

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