## experimentX 2 years ago A Question from my past paper: Use Residue theorem to prove $\int_0^\infty {\sin x \over x} = {\pi \over 2}$

1. mukushla

|dw:1346502102757:dw|

2. mukushla

|dw:1346502203118:dw|

3. experimentX

yep ... you are going in right direction.

4. mukushla

|dw:1346502289911:dw|

5. experimentX

Jordan's lemma :)

6. mukushla

|dw:1346502491432:dw|

7. mukushla

|dw:1346502593914:dw|

8. experimentX

hold on ... how did you get this |dw:1346503249095:dw|

9. mukushla

|dw:1346503481191:dw|

10. mukushla

|dw:1346503533199:dw|

11. experimentX

what did you apply man?

12. mukushla

oh sorry i was on another man

13. mukushla

$a_{-1}$is residue at $$z=0$$

14. experimentX

i mean how did you get that pi ... isn't it supposed to be 2pi?

15. mukushla

oh..ok

16. mukushla

if the tiny circle was full circle then it is 2pi but for semi-circle its pi

17. experimentX

thanks man!!

18. mukushla

see u santosh :)