## mahmit2012 3 years ago Q6 Find out the integral of log(sinx) in interval (0,pi/2].

1. mahmit2012

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2. akamushi

-1.08879

3. mahmit2012

solve it without calculator !!

4. akamushi

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

5. akamushi

then just plug in your interval

6. mahmit2012

are you sure? Ok check it out and then compare with your number.I think that is not true.

7. akamushi

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.

8. akamushi

i am sure of my anwser.

9. mahmit2012

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.

10. experimentX

i presume you are not looking for numerical methods

11. mahmit2012

yes especially for this interval we have an interesting way to find it out at regular calculus.

12. experimentX

is it approximate value??

13. experimentX
14. mahmit2012

no there is an exact value.i will show you next time.

15. experimentX

16. experimentX

this seems to give the same result http://www.wolframalpha.com/input/?i=integrate+x^2+cosec^2x%2F2+from+0+to+pi%2F2

17. mahmit2012

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18. mahmit2012

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19. mahmit2012

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20. mahmit2012

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