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lambchamps

  • 2 years ago

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

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  1. Freak7820
    • 2 years ago
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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. lambchamps
    • 2 years ago
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    can i do that, even if sin or cos is not raised two?

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

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

  5. lambchamps
    • 2 years ago
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    yea

  6. lambchamps
    • 2 years ago
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    i did that before

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

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

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

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

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

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

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

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

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

  16. lambchamps
    • 2 years ago
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    then distribute?

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

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

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

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

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

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

  23. hartnn
    • 2 years ago
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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

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

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