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suju101

integrate tan^3(x/4)*sec^2(x/4) from-2/3pi to pi help with the steps plz.

  • 2 years ago
  • 2 years ago

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  1. amistre64
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    since sec^2 is the derivaive of tan, this is a simple enough arrangement: \[\int f(u)du\]

    • 2 years ago
  2. amistre64
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    i thinkk you might be off by a 4 tho

    • 2 years ago
  3. amistre64
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    x/4 pops out a spurious little 1/4 that missing

    • 2 years ago
  4. shinigami1m
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    is -2pi/3 to pi = to pi to -2pi/3 ???

    • 2 years ago
  5. amistre64
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    then given the interval [a,b] you work it out: F(b)-F(a)

    • 2 years ago
  6. shinigami1m
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    @_@

    • 2 years ago
  7. shinigami1m
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    |dw:1326817635699:dw|

    • 2 years ago
  8. amistre64
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    \[[tan^4(\frac{1}{4}x)]'=\frac{1}{4}tan^3(\frac{1}{4}x)sec^2(\frac{1}{4}x)\] so we have to multiply thru by 4 to begin with

    • 2 years ago
  9. amistre64
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    |dw:1326817802065:dw|

    • 2 years ago
  10. TuringTest
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    \[u=\frac{x}{4}\to du=\frac{dx}{4}\to4du=dx\]\[\int_0}{|dw:1326817852162:dw|

    • 2 years ago
  11. suju101
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    \[\Pi ^{2}\div9{(65\Pi ^{2}/9)-26)}\] i got this ans. s this correct??i

    • 2 years ago
  12. amistre64
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    lol, I just derived tan^4(x/4) and got a spurious 1/4 so that cant be right

    • 2 years ago
  13. amistre64
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    hmmm, im off by something

    • 2 years ago
  14. amistre64
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    wolf agrees with turing

    • 2 years ago
  15. amistre64
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    oh yeah, the 4 pops out to get rid of the 1/4 lol

    • 2 years ago
  16. shinigami1m
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    derivative of (x/4) i think u miss it during derivative

    • 2 years ago
  17. TuringTest
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    yep, one comes out on top and bottom, so they cancel

    • 2 years ago
  18. amistre64
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    a was using an abacus ;)

    • 2 years ago
  19. TuringTest
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    lol

    • 2 years ago
  20. suju101
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    |dw:1326818150512:dw| i did this process n got that ans

    • 2 years ago
  21. TuringTest
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    is the problem\[\int_{\frac{-2\pi}{3}}^{\pi}\tan^3(\frac x4)\sec^2(\frac x4)dx\]?

    • 2 years ago
  22. suju101
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    yes

    • 2 years ago
  23. TuringTest
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    \[\int_{\frac{-2\pi}{3}}^{\pi}\tan^3(\frac x4)\sec^2(\frac x4)dx\]\[u=\frac x4\to du=\frac{dx}{4}\to4du=dx\]so...\[\int_{\frac{-2\pi}{3}}^{\pi}\tan^3(\frac x4)\sec^2(\frac x4)dx=4\int_{\frac{-\pi}{6}}^{\frac{\pi}{4}}\tan^3u\sec^2udu=4(\frac14\tan^4(\frac x4))|_{\frac{-2\pi}{3}}^{\pi}\]\[=\tan^4(\frac x4)|_{\frac{-2\pi}{3}}^{\pi}\]evaluate...

    • 2 years ago
  24. robtobey
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    \[\text{Tan}\left[\frac{\pi }{4}\right]^4-\text{Tan}\left[\frac{\frac{-2}{3}\pi }{4}\right]^4=\frac{8}{9} \]

    • 2 years ago
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