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anonymous

  • 5 years ago

integral from 0 to 6pi, 7theta^2(sin(1/12theta))dtheta

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  1. dumbcow
    • 5 years ago
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    integration by parts pull out the constant 7 first u = x^2 dv = sin(x/12) du = 2xdx v = -12sin(x/12)

  2. amistre64
    • 5 years ago
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    \[\int\limits_{0}^{6\pi} 7 \theta^2 \sin(\frac{1}{12} \theta) d \theta\] ??

  3. amistre64
    • 5 years ago
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    or is that (7t)^2 ??

  4. anonymous
    • 5 years ago
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    its right the first way u have it

  5. dumbcow
    • 5 years ago
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    = -12x^2cos(x/12) +24[integral xcos(x/12) dx] repeat integration by parts u = x dv = cos(x/12) du=dx v = 12sin(x/12)

  6. amistre64
    • 5 years ago
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    if i gotta repeat integrations; i just make a table to keep them organized

  7. anonymous
    • 5 years ago
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    if you express sin theta in eular's form then the integration will be easied

  8. anonymous
    • 5 years ago
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    yeh, but no one wants complex numbers in the answer geezzz

  9. amistre64
    • 5 years ago
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    v up ------------------------ u down | sin(t/12) ------------------------- + | t^2 | -cos(t/12) /12 ------------------------- - | 2t | -sin(t/12) / 144 ------------------------- + | t | cos(t/12)/ 144(12) ------------------------- 0 right?

  10. amistre64
    • 5 years ago
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    not to forget the 7 tho lol

  11. amistre64
    • 5 years ago
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    - 7t^2 cos(t/12) /12 + 14t sin(t/12) / 144 + 7t cos(t/12)/ 144(12) i think

  12. dumbcow
    • 5 years ago
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    amistre when you integrated the sin and cos, you multiplied the inside instead of dividing integral sin(ax) = -1/a*cos(ax) =7[-12x^2 cos(x/12) + 288x sin(x/12) + (24)(144)cos(x/12)]

  13. amistre64
    • 5 years ago
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    still rusty at integration by parts; thnx :)

  14. dumbcow
    • 5 years ago
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    no problem table is good idea though

  15. amistre64
    • 5 years ago
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    i seen the 12 and forgot it was a fraction :)

  16. anonymous
    • 5 years ago
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    thanks guys :)

  17. anonymous
    • 5 years ago
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    The derivative of \[7 \left(-1728 \left(-2+\frac{t^2}{144}\right) \text{Cos}\left[\frac{t}{12}\right]+288 t \text{Sin}\left[\frac{t}{12}\right]\right) \]is\[7 \left( 288 \text{ Sin}\left[\frac{t}{12}\right]+144 \left(-2+\frac{t^2}{144}\right) \text{Sin}\left[\frac{t}{12}\right]\right) \]simplified,\[7 t^2 \text{Sin}\left[\frac{t}{12}\right] \] The truth be told, I don't know how they did it.

  18. anonymous
    • 5 years ago
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    can u find the answer to integral of e^(6x) cos(7x)

  19. anonymous
    • 5 years ago
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    hold on.

  20. anonymous
    • 5 years ago
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    \[\int\limits e^{6 x} \text{Cos}[7 x]dx = \frac{1}{85} e^{6 x} (6 \text{Cos}[7 x]+7 \text{Sin}[7 x])+c \]Does OK?

  21. anonymous
    • 5 years ago
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    yes, thank u so much :)

  22. anonymous
    • 5 years ago
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    You might consider buying a Student version of Mathematica 8 if you intend to pursue a scientific or math career. At least you can verify your answers.

  23. anonymous
    • 5 years ago
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    there is wolframam alpha, google it, you can check answers on that for free

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