- #1
cloudboy
- 16
- 0
Homework Statement
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)
Homework Equations
M = [itex]\int[/itex] dm = [itex]\int[/itex]d(x)dA
Mx = [itex]\int[/itex]ydm
My = [itex]\int[/itex]xdm
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)(y2-2y+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!