Finding the Centroid of a Shaded Area with y=sqrt(x) Curve: Step-by-Step Guide"

[Bradracer18]

Homework Statement

I need to locate the centroid of the shaded area, in my picture. The shaded area is under the line(in between the x-axis and the curve.)

The curve is y=sqrt(x) And stretches a length from the y axis(0,0), along the x axis, a length of b.

This is a new concept, so I'm not really familiar with how to do these. It will probably take some walking through, for me to understand it.

Homework Equations

A = Int(dA)...not sure how to use integral, so will just use int.

X = int(xdA)

The Attempt at a Solution

I'm not sure how to find dA. I think I need to take a slice(or maybe 2) of the curved area. I'm not sure how to come up with those equations.

View attachment problem 5.bmp

 

[member 553083]

Then, I think that I need to find xdA, which I'm also not sure how to come up with. I'm assuming it's something like y times dx. But again, I'm not sure how to come up with the equation for that. After that, I think I would just integrate both of those equations, from 0 to b, and then divide the X equation by the A equation. Is this the correct approach? If so, what equation should I use for dA and xdA? Any help would be greatly appreciated. Thank you.