Find thecentroidof the area bounded by the curve

$\displaystyle

2y^2+2y-x-2=0

$

and the line $\displaystyle x=2y$.

http://img180.imageshack.us/img180/3669/centyr4.jpg

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- Feb 21st 2008, 06:37 AMcazimiCentroid problem
Find the

**centroid**of the area bounded by the curve

$\displaystyle

2y^2+2y-x-2=0

$

and the line $\displaystyle x=2y$.

http://img180.imageshack.us/img180/3669/centyr4.jpg - Feb 21st 2008, 08:10 AMwingless
Do you know how to double integrate?

$\displaystyle x=2y^2+2x-2$

$\displaystyle x=2y$

$\displaystyle \int \int ~dA$

Using $\displaystyle dA = dx~dy$ will be better. It'll be easier to apply the bounds for y, because the functions are y's functions.

A = $\displaystyle \int \int ~dx~dy$

M_x = $\displaystyle \int \int y ~dx~dy$

M_y = $\displaystyle \int \int x ~dx~dy$

$\displaystyle \bar {x} = \frac{M_y}{A}$

$\displaystyle \bar {y} = \frac{M_x}{A}$

And the centroid is $\displaystyle O(\bar {x},\bar {y})$.

Now apply the bounds and integrate and so on.. - Feb 21st 2008, 08:35 AMwingless
Here's another graph I made

http://img523.imageshack.us/img523/6...troidzzuz0.png