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

Question

anonymous · Answer

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tkhunny · Answer

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

anonymous · Answer

you have to do double integral to find mass right?

anonymous · Answer

so it will be (e-1)p?

tkhunny · Answer

Right, I assumed the very common uniform density.  Sorry abuot that.

"e-1"?  No.  How did you get that?

anonymous · Answer

im confused about setting out the integrals limits

anonymous · Answer

is it e(loge-1)

anonymous · Answer

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

tkhunny · Answer

$$\int\ln(x)\;dx = x\ln(x) - x + C$$

(e*ln(e) - e) - (1*ln(1) - 1) = e*ln(e) - e - 0 + 1 = e(1) - e + 1 = e-e+1 = 1

anonymous · Answer

what is that?
is that a mass?

tkhunny · Answer

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

anonymous · Answer

for the center mass the integral will be the same?

tkhunny · Answer

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,

anonymous · Answer

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

anonymous · Answer

just wanna know if this is the integration

tkhunny · Answer

Yes, that is one of them.