Originally Posted by

**Karl Harder** I have a question where it asks me to find the centre of mass in the x plane between 2 hemispheres where the centre of both hemispheres passes through the origin. The larger one has a radius A and the smaller one radius a. I have broken the area into 2 parts. A1 and A2.

For A1 the area used is between the 2 curves from origin to a (being the point where the smaller curve meets the line y=0)

$\displaystyle I_{x}=2\int_{0}^{a}(\sqrt{A^2-x^2}A^2-\sqrt{a^2-x^2}a^2)dx

$

For A2 the area used is between the curve from a to A (the area is between the larger hemisphere and y=0):

$\displaystyle I_{x}=2\int_{a}^{A}(\sqrt{A^2-x^2}A^2)dx

$

How then do you integrate the functions and then how do you substitute the limits a and A into the problem once you have integrated the functions? do you replace x with a and A?