Centroid - Ellipse

[m4ury91]

Find the centroid of the region in the first quadrant limited by the ellipse x2/a2 + y2/b2 = 1 and the line that intersects the positives extremes of the axis.

 

[m4ury91]

Find the centroid of the region in the first quadrant limited by the ellipse x2/a2+y2/b2 =1 and the line that intersects the positives extremes of the axis.

I was trying to solve that, but I need some help with that problem. Here is my progress so far:

 

[Dr.Peterson]

There are several things I expect to see here that I don't.

What is the equation of the straight line? You may just have a sign error here; but you never explicitly stated it.

What should you be integrating to find the x-coordinate of the centroid? Or are you so far only trying to find the area?

(To find the area, you could just use the known formulas for area of an ellipse and a triangle and subtract, though I suppose it's a good exercise to do it by integration. On the other hand, if you had done it geometrically too, you would see that there should be a pi in your answer.)

The biggest error I see is your integration of [MATH]\sqrt{a^2 - x^2}[/MATH], in which you failed to make a substitution correctly.

It will help if you describe in words what you are doing, and ask specific questions about it. It's hard to follow your unexplained work.

 

[Dr.Peterson]

Please don't submit the same question twice in different threads. Wait patiently for moderation and for responses ...

 

[MarkFL]

I've merged the two threads.