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anonymous

  • 5 years ago

how do you get a formula for an integral from 0 to pi of sine of theta raised to the power of 2n where n is an integer from 0?

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  1. anonymous
    • 5 years ago
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    \[\int\limits_{0}^{\Pi}\sin ^{2n}(\theta)d \theta\]

  2. anonymous
    • 5 years ago
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    2n+1 is the exponent and the denomater is 2n+1

  3. anonymous
    • 5 years ago
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    actually i think thats wrong sry ill look it up

  4. anonymous
    • 5 years ago
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    The answer is \[\Pi(2n)!/((2^{2n})\times (n!)^{2})\]

  5. anonymous
    • 5 years ago
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    but how do you get to that?

  6. anonymous
    • 5 years ago
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    So I know that e^(i*pi/2)= i

  7. anonymous
    • 5 years ago
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    and e^(i(theta)) = cos(theta)+ isin(theta)

  8. anonymous
    • 5 years ago
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    also cos(theta)= (e^(itheta)+e^(-itheta))/2 and sin(theta)=(e^(itheta)-e^(-itheta))/(2i)

  9. anonymous
    • 5 years ago
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    There is also an identity, 2cos(theta)e^(itheta)=1+e^(i2theta)

  10. anonymous
    • 5 years ago
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    You there?

  11. anonymous
    • 5 years ago
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    yea chill im just trying to figure it out

  12. anonymous
    • 5 years ago
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    Moo is using De Moivre's Theorem

  13. anonymous
    • 5 years ago
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    Exactly!

  14. anonymous
    • 5 years ago
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    Then.....?

  15. anonymous
    • 5 years ago
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    also not to mention, \[\int\limits_{0}^{\Pi}\cos \theta ^{n}\cos n \theta d \theta=\Pi/2^{n}, n =0\]

  16. anonymous
    • 5 years ago
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    n=0, 1, 2, 3....

  17. anonymous
    • 5 years ago
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    this might also be a hint, but e^(i*2pi*k) where k is any integer is 1. (for reasons I fully don't know)

  18. anonymous
    • 5 years ago
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    Whats your major Moo?

  19. anonymous
    • 5 years ago
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    english

  20. anonymous
    • 5 years ago
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    contemporary american drama

  21. anonymous
    • 5 years ago
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    you know an awful lot about calculus for an English major..... lol

  22. anonymous
    • 5 years ago
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    read Oleanna, Third, ah...Shape of things and such. You know calculus is really fun

  23. anonymous
    • 5 years ago
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    so rewrite the integrand as sin(theta)*sin(theta) both raised to the power n?

  24. anonymous
    • 5 years ago
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    calculus is legit

  25. anonymous
    • 5 years ago
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    also is cos(n*theta)=cos(theta)^n? Yeah, it is..lol.

  26. anonymous
    • 5 years ago
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    oh, bedtime. my mom is calling me downstairs with her awful hammer thingie.

  27. anonymous
    • 5 years ago
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    Thanks a lot guys.

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