## math_proof Group Title find centroid of the region bounded by y=ln(x) the axis and x=e one year ago one year ago

1. math_proof

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2. tkhunny

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

3. math_proof

you have to do double integral to find mass right?

4. math_proof

so it will be (e-1)p?

5. tkhunny

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

6. math_proof

im confused about setting out the integrals limits

7. math_proof

is it e(loge-1)

8. math_proof

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

9. tkhunny

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

10. math_proof

what is that? is that a mass?

11. tkhunny

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

12. math_proof

for the center mass the integral will be the same?

13. tkhunny

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,

14. math_proof

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

15. math_proof

just wanna know if this is the integration

16. tkhunny

Yes, that is one of them.