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Have you considered setting up the integral?

yes I did

What did you set up?

v = ∫[0,lnπ] π sin^2(e^x) dx

not sure if thats correct

Are you sure it's finite?

I think so

its the volume bounded by two graphs so im pretty sure

Good. Do you believe there is a nice, closed-form expression for the integral?

yes

do you think the integral I set up is correct?

Your integral looks fine.
Are you sure this isn't an integral for numerical methods?

Not sure

it is a definite integral

??