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anonymous
 one year ago
The region in the first quadrant bounded by the xaxis, the line x = ln(π), and the curve y = sin(ex) is rotated about the xaxis. What is the volume of the generated solid?
anonymous
 one year ago
The region in the first quadrant bounded by the xaxis, the line x = ln(π), and the curve y = sin(ex) is rotated about the xaxis. What is the volume of the generated solid?

This Question is Closed

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.0Have you considered setting up the integral?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0v = ∫[0,lnπ] π sin^2(e^x) dx

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0not sure if thats correct

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.0Are you sure it's finite?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0its the volume bounded by two graphs so im pretty sure

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.0Good. Do you believe there is a nice, closedform expression for the integral?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0do you think the integral I set up is correct?

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.0Your integral looks fine. Are you sure this isn't an integral for numerical methods?

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.0Okay, 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?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0it is a definite integral

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.0Well, 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?

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.0There is a lot of information on the "Sine Integral". http://mathworld.wolfram.com/SineIntegral.html No easy form as a result.
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