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lambchamps Group Title

int. calculus \[\int\limits_{}^{}\sin ^{2}x \cos ^{2}x \tan ^{2} x dx\]

  • 2 years ago
  • 2 years ago

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  1. Freak7820 Group Title
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    Write them as sin squared x = (1/2)(1 - cos 2x) cos squared x = (1/2)(1 + cos 2x) maybe..that'll be easier for you to integrate.

    • 2 years ago
  2. lambchamps Group Title
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    can i do that, even if sin or cos is not raised two?

    • 2 years ago
  3. hartnn Group Title
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    doesn't that simplify to sin^4 x when tan is written as sin/cos ?

    • 2 years ago
  4. SheldonEinstein Group Title
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    Write tan^2 x = sin^2 x / cos^2 x

    • 2 years ago
  5. lambchamps Group Title
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    yea

    • 2 years ago
  6. lambchamps Group Title
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    i did that before

    • 2 years ago
  7. SheldonEinstein Group Title
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    \[\large{\int { sin^4x dx}}\] Can you do this?

    • 2 years ago
  8. lambchamps Group Title
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    then i lost any of ideas after that

    • 2 years ago
  9. SheldonEinstein Group Title
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    OK no problem, where are you lost?

    • 2 years ago
  10. hartnn Group Title
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    can u integrate sin^2 x ?

    • 2 years ago
  11. lambchamps Group Title
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    after i got the \[\int\limits_{?}^{?}\sin ^{4}xdx\]

    • 2 years ago
  12. SheldonEinstein Group Title
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    Well if integration of sin x dx= -cosx + C then that of sin^4 x dx = ?

    • 2 years ago
  13. lambchamps Group Title
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    -cos^4x + C ??

    • 2 years ago
  14. hartnn Group Title
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    write sin^4 x = (sin^2 x)(1-cos^2 x)

    • 2 years ago
  15. hartnn Group Title
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    no, its not that direct

    • 2 years ago
  16. lambchamps Group Title
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    then distribute?

    • 2 years ago
  17. hartnn Group Title
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    = (sin^2 x)(1-cos^2 x) = sin^2 x - sin^2x cos^2 x yes

    • 2 years ago
  18. hartnn Group Title
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    = sin^2 x - sin^2x cos^2 x = sin^2 x - (1/4) (sin 2x)^2

    • 2 years ago
  19. lambchamps Group Title
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    how did you get (1/4)(sin 2x)^2?

    • 2 years ago
  20. hartnn Group Title
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    sin 2x = 2 sin x cos x to get sin^2x cos^2 x , i squared the above .....

    • 2 years ago
  21. hartnn Group Title
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    got that ? ^ and can u integrate sin^2 x - (1/4) (sin 2x)^2

    • 2 years ago
  22. lambchamps Group Title
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    can you show me the whole process of that sin 2x = 2 sin x cos x

    • 2 years ago
  23. hartnn Group Title
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    u want me to prove 2sin x cos x = sin 2x or u wanted this : sin 2x = 2 sin x cos x (sin 2x)^2 = (2 sin x cos x)^2 = 4 sin^2x cos^2 x so sin^2 x cos^2 x = (1/4) (sin 2x)^2

    • 2 years ago
  24. hartnn Group Title
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    so if u can integrate sin^2 x you can also integrate sin^2 x - (1/4) (sin 2x)^2

    • 2 years ago
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