Finding Y-Bar for a Constant Density Region

[whatlifeforme]

Homework Statement

constant density. region bounded by y=x-x^2, y=-x.

Homework Equations

this is according to the formula my instructor gave me:

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

The Attempt at a Solution

Y(bar) = (1/2) (integral)(0 to 2) [ δ ((x-x^2)^2 - (-x)^2) dx ]
----------------------------------------------------
(integral)(0 to 2) [δ ((x-x^2) - (-x)) dx]

(1/2)(integral) (0 to 2) [δ (-2x^2 + x^4) dx ] = 8δ/15
(integral)(0 to 2) [δ ((x-x^2) - (-x)) dx] = 4δ/3

Y(bar) = 2/5 ; however, the answer is -3/5.

 

[whatlifeforme]

sorry. solved.