Find the x=-corrdinate of the centroid...

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nikchic5

Junior Member
Joined
Feb 16, 2006
Messages
106
Please help...
Find the x-coordinate of the centriod of the region bounded by the graphs of y=cubed root of x, y=0, and x=8.

So far I got
m=p int [0,6] cubed root of x dw= p int[0,6] x^1/3 dx
which I belive is
p[(x^4/3) / (4/3) ] is that right on the integration?

Sorry Ive been studying so long Im losing my mind!! I end up getting 32 but the correct answer is 32/7 can someone please help me in letting me know what I am doing wrong??

Thanks so much!
 
I do not understand your notation. What's "p"? What does "dw" mean with 'x' in the arguement?

What was your value for M after performing this integration?

What was your integration setup to determine the Numerator for the x-coordinate?

If you learned just a little LaTeX, we all would get along a lot better. Just a couple of simple codes will produce this:

\(\displaystyle \L\;\int_{0}^{8}{\sqrt[3]{x}}\;dx\)

I expect it is easier than you might think.
 
Follow up question..

I am sorry I do not know how to do that. p means rho which is the greek letter. and I didn't mean dw I meant dx sorry.
The value for m that I got was 324 rho but I do not think that is correct.
Where am I going wrong?
 
Hello nikchic:

\(\displaystyle \L\\A=\int_{0}^{8}\int_{0}^{x^{\frac{1}{3}}}dydx\)

\(\displaystyle \L\\\overline{x}=\frac{1}{A}\int_{0}^{8}\int_{0}^{x^{\frac{1}{3}}}xdydx\)

\(\displaystyle \L\\\overline{y}=\frac{1}{A}\int_{0}^{8}\int_{0}^{x^{\frac{1}{3}}}ydydx\)
 
Re: Follow up question..

nikchic5 said:
I am sorry I do not know how to do that.
Click to expand...
If you take a really close look, you will see that I extended an invitation for you to LEARN how to do it. Please do not discard the invitation with a simple denial.
 
Sorry about that....

Oh sorry I did not realize that. Anyways this is what I have so far. I am going to try to type it the right way

\(\displaystyle m=\rho \int_{0}^{8}{\sqrt[3]{x}}\;dx = \rho \int_{0}^{8}{x^{\frac{1}{3}} \;dx\)

from there I get 12 rho which I then plug into the my equation and I get 384 rho.

Then I divided the two and got 32...but the answer is x=32/7
so I was wondering what I did wrong?

Edit: You were so close. Just select your coding and click on the TeX button. Also, put a slash in front of the names of greek letters. Finally, make sure your exponents are completely enclosed in brace pairs. These are the only modifications I made.
 
Did you pay any attention to what I gave you. That's everything but the direct answer.
 
12 is good. You'll have to show your equation for the rest. Something is fishy in there.
 
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