Thin Plates with Constant Density (Calculus II)

[dm41nes]

Thank you in advance for the help!

Homework Statement

Find the center of mass of a thin plate of constant density (delta) covering the given region.
The region bounded by the parabola y= x - x² and the line y= -x

Homework Equations

See attachment question 15 p1

The Attempt at a Solution

See attachment question 15 p2

 

[luvlybug1025]

I like your last solution on attachment 2 except...
Integral from 0 to 2 (x-x^2-x) dx is not Int (2x - x^2) dx
I think you just have an algebra mistake there.

 

[dm41nes]

Thank you, well it was x-x^2-(-x). So, I added the double negative to the other x. Thats how I was able to get 2x.


Are these forumulas a certified way to find the center of mass?