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

you have to do double integral to find mass right?

so it will be (e-1)p?

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

im confused about setting out the integrals limits

is it e(loge-1)

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

what is that?
is that a mass?

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

for the center mass the integral will be the same?

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

just wanna know if this is the integration

Yes, that is one of them.