centroid of a semi ellipse

[saaraneth]

I've been working on this problem for 3+ hours, and with an English term paper due on Monday, I give up. Help!

The QuestionFind the centroid of the semi-elliptical region defined by

Comments

[profhauke]

When I look at your integral, it seems you're multiplying x by the equation for the top half of the region you're interested in, so you'd be finding the centroid of the upper right quarter of the ellipse (where x>0 and y>0) not the centroid of the right half of the ellipse (where just x>0).

As to how to do it, what's the derivative of u = 1-(x/a)^2?

[saaraneth]

oh. So to find it for the right half of the ellipse, where x>0...do I multiply the b*sqaureRoot(1-(x/a)) by 2?

the derivative of u = 1-(x/a)^2 should be du/dx=-(2/a^2)x or is it something to do with trig because I'm bad at that?

thanks for your help. =D

[profhauke]

Yes, you'd multiply by 2. Also, I was trying to hint at a u substitution you might try, without giving it away totally. Do you see how it'd work?

[saaraneth]

Oh wow. I got it. Thank you so much!