anonymous
  • anonymous
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?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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tkhunny
  • tkhunny
Have you considered setting up the integral?
anonymous
  • anonymous
yes I did
tkhunny
  • tkhunny
What did you set up?

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More answers

anonymous
  • anonymous
v = ∫[0,lnπ] π sin^2(e^x) dx
anonymous
  • anonymous
not sure if thats correct
tkhunny
  • tkhunny
Are you sure it's finite?
anonymous
  • anonymous
I think so
anonymous
  • anonymous
its the volume bounded by two graphs so im pretty sure
tkhunny
  • tkhunny
Good. Do you believe there is a nice, closed-form expression for the integral?
anonymous
  • anonymous
yes
anonymous
  • anonymous
do you think the integral I set up is correct?
tkhunny
  • tkhunny
Your integral looks fine. Are you sure this isn't an integral for numerical methods?
anonymous
  • anonymous
Not sure
tkhunny
  • tkhunny
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?
anonymous
  • anonymous
it is a definite integral
tkhunny
  • tkhunny
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?
anonymous
  • anonymous
??
tkhunny
  • tkhunny
There 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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