(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Set up integrals to find M, Mx, and My for the thin plate if d(x)=ky

bounded by y=2-x and y = 4-x^2 or x = sqrt(4-y)

2. Relevant equations

M = [itex]\int[/itex] dm = [itex]\int[/itex]d(x)dA

Mx = [itex]\int[/itex]ydm

My = [itex]\int[/itex]xdm

3. The attempt at a solution

I broke this down into three equations. x1 = 2-y; x2 = -sqrt(4-y), x3= sqrt(4-y)

I used horizontal elements so that d(x) is constant across the entire element.

When calculating M, I got [itex]\int[/itex](ky)(x2-x1)dy = [itex]\int[/itex](0→3)(ky)(sqrt(4-y))-(2-y)dy + [itex]\int[/itex](3→4)(ky)(sqrt(4-y))-(-sqrt(4-y))dy

I got this down to:

k[itex]\int[/itex](0→3)(y^{2}-2y+ysqrt(4-y))dy + 2k[itex]\int[/itex](3→4)(ysqrt(4-y))dy

The problem is basically that I can't figure out how to integrate these to find the total mass. Please help thanks!

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# Homework Help: Find M, Mx, and My for a thin plate if density=ky

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