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find centroid of the region bounded by y=ln(x) the axis and x=e



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dw:1352954819183:dw

tkhunny
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First, you'll need the total area. What do you get?

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you have to do double integral to find mass right?

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so it will be (e1)p?

tkhunny
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Right, I assumed the very common uniform density. Sorry abuot that.
"e1"? No. How did you get that?

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im confused about setting out the integrals limits

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is it e(loge1)

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\[\int\limits_{1}^{e}\int\limits_{0}^{\ln(x)}p dydx\]

tkhunny
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\[\int\ln(x)\;dx = x\ln(x)  x + C\]
(e*ln(e)  e)  (1*ln(1)  1) = e*ln(e)  e  0 + 1 = e(1)  e + 1 = ee+1 = 1

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what is that?
is that a mass?

tkhunny
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\[\int_{1}^{e}\int_{0}^{ln(x)}\rho\;dy\;dx = \rho\]

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for the center mass the integral will be the same?

tkhunny
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It's not a matter of guesing or whether we can predict it or how we feel about it. It's just how it works out on this one,

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\[\int\limits_{1}^{e}\int\limits_{0}^{\ln(x)}xpdydx\]

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just wanna know if this is the integration

tkhunny
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Yes, that is one of them.