walters 2 years ago compute the following integral

1. walters

$\int\limits_{\pi}^{\pi}\frac{ 1}{ 1+e ^{sinx} }dx$

2. cluo

its from pi to pi?

3. walters

oh from -pi to pi

4. walters

i only have the finaly answer (pi) but i don'tknow did they it

5. cluo

what level is this?

6. walters

second

7. cluo

second what?

8. walters

ok maybe i don't understand u which level are u refering to?

9. cluo

10. walters

11. cluo

past vector calculus?

12. walters

i did pure calculus now is the second level of it (which is advanced calculus)

13. cluo

have you done double and triple integrals? i only ask because i think i saw something similar a couple days ago.

14. walters

i am not sure whether this is possible The substitution of x=-y yields |dw:1360491262699:dw| NB:not sure

15. walters

@phi pls help

16. hartnn

do you know a standard integral... $$\int \limits_a^b f(x)dx =\int \limits_a^b f(a+b-x)dx$$

17. hartnn

*standard property.

18. walters

no

19. hartnn

ok, then do you want to use this (1 method) or continue with what u did (another method) of putting x=-y...

20. walters

any method u know u can use it i'll try to catch up

21. hartnn

ok, i'll tell u both, first using your substitution x=-y, |dw:1360492675542:dw| |dw:1360492681874:dw| understood till here ?

22. walters

ok this means i will have |dw:1360492779070:dw| @hartnn can u pls teach me/explain standard property

23. hartnn

yes, you got it correct using your method, now the standard property... let I = integral ..... -------->(1) now using that property, first tell what is a+b-x =.... ?

24. walters

pi-pi-x=-x

25. hartnn

yes, so, because of that property, |dw:1360493289196:dw| add 1 and 2 what u get ?

26. walters

|dw:1360493238315:dw|

27. walters

from -pi to pi

28. hartnn

umm...not actually.... |dw:1360493484296:dw| |dw:1360493501827:dw| s = sin x

29. hartnn

|dw:1360493565788:dw|

30. hartnn

got that ^ ?

31. walters

wow i see now so tell me how wil i know that i must use standart property

32. hartnn

thats trial and error, i first thought of substitution, then recalled different properties, then this property was found to be useful...wih enough practice, this procedure becomes easy and fast...

33. hartnn

also you must know all the properties beforehand ...

34. walters

ok thnx

35. hartnn

welcome ^_^

36. walters

@jacobian see this