Find the center of mass of a thin plate of constant density

[whatlifeforme]

Homework Statement

Find the center of mass of a thin plate of constant density (δ covering the triangular region in this first quadrant between the circle x^2 + y^2 = 4 and the lines x=2 ; y=2.

Homework Equations

x^2 + y^2 = 4 and the lines x=2 ; y=2.

The Attempt at a Solution

x(bar) = integral(a to b) δ x (f(x) - g(x)) dx
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integral(a to b) δ (f(x) - g(x)) dx

y(bar) = (1/2) integral(a to b) δ (f(x)^2 - g(x)^2) dx
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integral(a to b) δ (f(x) - g(x)) dx

I am not sure how to start with this problem. should i solve for y first?

 

[Dick]

Draw a sketch of the region first. Then figure out what curve f(x) is on the top of your region and which what curve g(x) is on the bottom. And sure, to describe one of them you need to solve for y.

 

[whatlifeforme]

thanks. solved.