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anonymous

  • one year ago

The region in the first quadrant bounded by the x-axis, the line x = π, and the curve y = sin(sin(x)) is rotated about the x-axis. What is the volume of the generated solid?

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  1. anonymous
    • one year ago
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    my main trouble is finding the area bounded by the functions

  2. freckles
    • one year ago
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    |dw:1438886124740:dw| looks something like that

  3. freckles
    • one year ago
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    well the area bounded by x=0 and x=pi and y=sin(sin(x) and y=0

  4. anonymous
    • one year ago
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    x = pi !!! i see for some reason i just assumed it was y = pi

  5. freckles
    • one year ago
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    y=sin(sin(x))* forgot to close the parenthesis

  6. anonymous
    • one year ago
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    okay so this area right |dw:1438886325934:dw|

  7. freckles
    • one year ago
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    they want you to find the volume of that thing rotated about y=0? or just find the integral representation fro the volume?

  8. anonymous
    • one year ago
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    the former

  9. freckles
    • one year ago
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    have you ever heard of the bessel function?

  10. anonymous
    • one year ago
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    i have now

  11. anonymous
    • one year ago
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    let me try to do the problem and tell me if i did something wrong

  12. freckles
    • one year ago
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    alright just so we are clear that one equation is y=sin(sin(x))?

  13. freckles
    • one year ago
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    if so i have some research to do :p unless we can use some form of approximating maybe like taylor series

  14. anonymous
    • one year ago
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    yes it is y= sin(sin(x)) but if your wondering i'm rather certain the x intercept happens to be at pi

  15. anonymous
    • one year ago
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    its just calc 1 so should not involve anything too complex

  16. freckles
    • one year ago
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    i'm just extremely curious how we are going to evaluate: \[\int\limits_{0}^{\pi} \pi \sin^2(\sin(x)) dx\] it involves non-elementary functions

  17. anonymous
    • one year ago
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    well ill just use the trusty ti-84 :D

  18. freckles
    • one year ago
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    ok so that is awesome if we can use calculator

  19. anonymous
    • one year ago
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    1.219

  20. freckles
    • one year ago
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    I'm not getting that

  21. anonymous
    • one year ago
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    what are you getting ?

  22. anonymous
    • one year ago
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    oh woops forgot to multiply by pi

  23. freckles
    • one year ago
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    http://www.wolframalpha.com/input/?i=integrate%28pi*sin%5E2%28sin%28x%29%29%2Cx%3D0..pi%29 approximately 3.83

  24. anonymous
    • one year ago
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    close one 1.219 is an answer choice too

  25. freckles
    • one year ago
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    lol they were probably like oooo let's throw in a trick choice the answer sorta you know just without being multiplied by pi

  26. anonymous
    • one year ago
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    yep almost fell right for it , thanks for catching me :D

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