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- #1

- Jan 17, 2013

- 1,667

[tex]\int_{\alpha}^{\beta} \, f(\gamma (t))\, \gamma '(t) \, dt [/tex]

[tex]\text{Use the substitution : } \gamma (t) = \xi [/tex]

[tex]\int_{\gamma (\alpha) }^{\gamma (\beta)} \, f(\xi )\, d \xi [/tex]

[tex]\text{If we integrate around a closed loope : }\gamma (\alpha) = \gamma(\beta) [/tex]

[tex]\int_{\gamma (\alpha) }^{\gamma (\alpha)} \, f( \xi )\, d \xi =0 [/tex]

[tex]\text{This is only true if the function is analytic }[/tex]

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