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experimentX

  • 2 years ago

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

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  1. mukushla
    • 2 years ago
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    |dw:1346502102757:dw|

  2. mukushla
    • 2 years ago
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    |dw:1346502203118:dw|

  3. experimentX
    • 2 years ago
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    yep ... you are going in right direction.

  4. mukushla
    • 2 years ago
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    |dw:1346502289911:dw|

  5. experimentX
    • 2 years ago
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    Jordan's lemma :)

  6. mukushla
    • 2 years ago
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    |dw:1346502491432:dw|

  7. mukushla
    • 2 years ago
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    |dw:1346502593914:dw|

  8. experimentX
    • 2 years ago
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    hold on ... how did you get this |dw:1346503249095:dw|

  9. mukushla
    • 2 years ago
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    |dw:1346503481191:dw|

  10. mukushla
    • 2 years ago
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    |dw:1346503533199:dw|

  11. experimentX
    • 2 years ago
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    what did you apply man?

  12. mukushla
    • 2 years ago
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    oh sorry i was on another man

  13. mukushla
    • 2 years ago
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    \[a_{-1}\]is residue at \(z=0\)

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

  15. mukushla
    • 2 years ago
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    oh..ok

  16. mukushla
    • 2 years ago
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    if the tiny circle was full circle then it is 2pi but for semi-circle its pi

  17. experimentX
    • 2 years ago
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    thanks man!!

  18. mukushla
    • 2 years ago
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    see u santosh :)

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