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anonymous

  • one year ago

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?

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  1. tkhunny
    • one year ago
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    Have you considered setting up the integral?

  2. anonymous
    • one year ago
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    yes I did

  3. tkhunny
    • one year ago
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    What did you set up?

  4. anonymous
    • one year ago
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    v = ∫[0,lnπ] π sin^2(e^x) dx

  5. anonymous
    • one year ago
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    not sure if thats correct

  6. tkhunny
    • one year ago
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    Are you sure it's finite?

  7. anonymous
    • one year ago
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    I think so

  8. anonymous
    • one year ago
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    its the volume bounded by two graphs so im pretty sure

  9. tkhunny
    • one year ago
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    Good. Do you believe there is a nice, closed-form expression for the integral?

  10. anonymous
    • one year ago
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    yes

  11. anonymous
    • one year ago
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    do you think the integral I set up is correct?

  12. tkhunny
    • one year ago
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    Your integral looks fine. Are you sure this isn't an integral for numerical methods?

  13. anonymous
    • one year ago
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    Not sure

  14. tkhunny
    • one year ago
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    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?

  15. anonymous
    • one year ago
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    it is a definite integral

  16. tkhunny
    • one year ago
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    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?

  17. anonymous
    • one year ago
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    ??

  18. tkhunny
    • one year ago
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    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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