The region in the first quadrant bounded by the x-axis, the line x = ln(π), and the curve y = sin(ex) is rotated about the x-axis. What is the volume of the generated solid?
Stacey Warren - Expert brainly.com
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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?
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?
Okay, one more question. Is it a Definite Integral? In other words, does it actually exist at x = 0 or is that a limit behavior we need to worry about?
it is a definite integral
Well, I believe we are out of luck on this one. With a little transformation (t = e^x), we can make this one look like sin(t)/t, and that's not encouraging.
It's time for numerical methods. What tools have you?
There is a lot of information on the "Sine Integral".
No easy form as a result.