Draw a 3 m x 3 m square. On the diagonal is a line corner to corner: y=x. Under that is a line enclosing a area with the function y=x^3/9.

How is the steps to integrate y bar: (integ $y dA) /(integ $ dA)

EinsteinAlbert
Mar 17, 2015

#1**+5 **

I assume you want to find the area between y= x and y =x^3/9

We have

3

∫ x - x^3/9 dx =

0

[x^2/2 - (1/36)x^4] from 0 to 3 = [3^2/2 - (1/36)3^4 ]= 9/2 - 81/36 = [162 - 81] / 36 = 81/36 = 9/4 = 2.25 sq units

CPhill
Mar 17, 2015

#2**+10 **

Best Answer

Here's another interpretation of the question:

However, this interpretation makes the Y(x) = x somewhat irrelevant, so it's quite possible this is not what was wanted!

.

Alan
Mar 18, 2015

#3**0 **

Where does y2+((y1-y2)/2) dy = dA come into the workings shown by CPhill?

EinsteinAlbert
Mar 21, 2015

#4**0 **

Also was his answer showing the equation for numerator and denominator or just the numerator? Seems like the later.

EinsteinAlbert
Mar 21, 2015

#5**0 **

I want the centroid location x bar and y bar of the uncommon area. I don't think it has been answered right.

EinsteinAlbert
Mar 21, 2015

#6**+5 **

hi Albert,

My answers keep disappearing - I shall try again

I did not answer this in the first place because I did not understand the question.

DO YOU want to find the area between the curves $$y=x \;\;and\;\; y=\frac{x^3}{9}$$ for x=0 to x=3 ?

(I think that this was CPhill's assumption)

[You were logged on when I published this :/ ]

Melody
Mar 21, 2015

#7**+5 **

If it's the coordinates of the centroid of the area between the two curves that you want, then see the following:

.

Alan
Mar 21, 2015

#8**+5 **

What the * H**L*???

How was I supposed to know * WHAT* you wanted???

I certainly didn't see the word "centroid" anywhere in your question...!!!

I thought you were wanting the area between the curves {silly assumption on my part...}

If you want a specific thing......maybe you should* INCLUDE* that specific thing when you post.....!!!!

CPhill
Mar 21, 2015

#9**0 **

Hear, hear Chris! I agree !!

We are not paid to be mindreaders - oh, I just remembered, we are not paid at all! LOL

I still have to assimilate what a centroid is exactly.

Melody
Mar 21, 2015

#10**+5 **

Melody, if we have a plane of equal thickness, the centroid can be thought of as the "balance point" of the plane.

CPhill
Mar 21, 2015

#11**0 **

I should have specified the area between.

Y bar and equation for the location of the centroid in the Y axis is writen in my question. All answers were fine and helpful. The inside area makes sense and makes a good assumption CPhill.

And how much posts have you all answered, if you had a question you could ask and simply wait for a reply or ask for terms such as y bar to be clarified. We are all at fault here but sarcasm ain't friendly.

I can understand it now from answers Cheers.

EinsteinAlbert
Mar 21, 2015