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mahmit2012
Q6 Find out the integral of log(sinx) in interval (0,pi/2].
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solve it without calculator !!
integral log(sin(x)) dx = 1/2 i (x^2+Li_2(e^(2 i x)))-x log(1-e^(2 i x))+x log(sin(x))+constant
then just plug in your interval
are you sure? Ok check it out and then compare with your number.I think that is not true.
this is a difficult integrand, perhaps i don't remember a short cut. i doubt an instructor would ask this question with out one, especially at lower level calculus.
i am sure of my anwser.
ok please write your formula in a blank I check it out myself and will show you it is not correct.because there is no close function for this integral.
i presume you are not looking for numerical methods
yes especially for this interval we have an interesting way to find it out at regular calculus.
is it approximate value??
http://www.wolframalpha.com/input/?i=cos+x+plot+from+0+to+pi%2F2 http://www.wolframalpha.com/input/?i=cos+x+plot+from+0+to+pi%2F2 they both seem similar !!
no there is an exact value.i will show you next time.
something interesting about http://www.wolframalpha.com/input/?i=integrate+x+cotx+from+0+to+pi%2F2
this seems to give the same result http://www.wolframalpha.com/input/?i=integrate+x^2+cosec^2x%2F2+from+0+to+pi%2F2
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