Question

Find the exact coordinates of the centroid for the region bounded by the curves y=x+2 and y=x^2.

Answer 1

I already found the x coordinate, but how do you find the y coordinate?

Answer 2

It's from pretty little liars.

Answer 3

y =x+2 is above y = x\(^2\) in the interval [-1, 2]
(you can sketch the graph and check those points).


Centroid = (xbar, ybar)
where xbar =\(\sf \color{}{\frac{M_y}{A}}\) and ybar = \(\sf \color{}{\frac{M_x}{A}}\)

With
M\(_y\) = [ x (f(x) - g(x)) dx ] from -1<x<2
and same for

M\(_x\) = ∫[ \(\sf \color{}{\frac{1}{2}}\) ((f(x))\(^2\) - (g(x))\(^2\)dx on -1<x<2

Answer 4

i already found xbar = \[\frac{ \int\limits\limits_{-1}^{-2}x(x+2-x^2)dx }{ \int\limits\limits_{-1}^{2}(x+2-x^2)dx }\] = 0.5 :)
i just need to find ybar, which i'm not really sure how to find :(