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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?
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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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{0}^{\Pi}\sin ^{2n}(\theta)d \theta\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.02n+1 is the exponent and the denomater is 2n+1

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0actually i think thats wrong sry ill look it up

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The answer is \[\Pi(2n)!/((2^{2n})\times (n!)^{2})\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but how do you get to that?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So I know that e^(i*pi/2)= i

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and e^(i(theta)) = cos(theta)+ isin(theta)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0also cos(theta)= (e^(itheta)+e^(itheta))/2 and sin(theta)=(e^(itheta)e^(itheta))/(2i)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0There is also an identity, 2cos(theta)e^(itheta)=1+e^(i2theta)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yea chill im just trying to figure it out

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Moo is using De Moivre's Theorem

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0also not to mention, \[\int\limits_{0}^{\Pi}\cos \theta ^{n}\cos n \theta d \theta=\Pi/2^{n}, n =0\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0this might also be a hint, but e^(i*2pi*k) where k is any integer is 1. (for reasons I fully don't know)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Whats your major Moo?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0contemporary american drama

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you know an awful lot about calculus for an English major..... lol

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0read Oleanna, Third, ah...Shape of things and such. You know calculus is really fun

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so rewrite the integrand as sin(theta)*sin(theta) both raised to the power n?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0also is cos(n*theta)=cos(theta)^n? Yeah, it is..lol.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh, bedtime. my mom is calling me downstairs with her awful hammer thingie.
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