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# Integration

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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)

Mar 17, 2015

#2
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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!

.

Mar 18, 2015

#1
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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

Mar 17, 2015
#2
+27377
+10

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

Mar 21, 2015
#4
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Also was his answer showing the equation for numerator and denominator or just the numerator? Seems like the later.

Mar 21, 2015
#5
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I want the centroid location x bar and y bar of the uncommon area. I don't think it has been answered right.

Mar 21, 2015
#6
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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 :/  ]

Mar 21, 2015
#7
+27377
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If it's the coordinates of the centroid of the area between the two curves that you want, then see the following:

.

Mar 21, 2015
#8
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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.....!!!!

Mar 21, 2015
#9
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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.

Mar 21, 2015
#10
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Melody, if we have a plane of equal thickness,  the centroid can be thought of as the "balance point" of the plane.

Mar 21, 2015
#11
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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.

Mar 21, 2015