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



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mukushla
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dw:1346502102757:dw

mukushla
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dw:1346502203118:dw

experimentX
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yep ... you are going in right direction.

mukushla
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experimentX
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Jordan's lemma :)

mukushla
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mukushla
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dw:1346502593914:dw

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

mukushla
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mukushla
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experimentX
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what did you apply man?

mukushla
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oh sorry i was on another man

mukushla
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\[a_{1}\]is residue at \(z=0\)

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

mukushla
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oh..ok

mukushla
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if the tiny circle was full circle then it is 2pi but for semicircle its pi

experimentX
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thanks man!!

mukushla
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see u santosh :)