From Example Problems
Jump to: navigation, search

nasty home movie ankeny iowa movie theater madagascar production design movie movie parent review alpha step show videos nero6606 serial no. entertainment movie movie portal showtimes as funny hell movie eplan 5.60 crack singing parrot video movies to watch on the computer reo speedwagon video sunny leone free movies url american journal of respiratory and critical medicine radeon x1600 pro video card agp romanian dance song video apollo video technology in car system agreement end license user mentos commercial video lick pussy video free sex movie cinema paint shop pro cracked make believe torrent top domain alabama land surveying license movie and tv sound clip military police video skin to win video movie studio pro marriage license in orange county ca asylum card video kelly movie r domain emporium joblo movie map mark wills videos quantum leap movie 2005 music video code for turn it up la tortura video albuquerque movie west rasputin movie review sarah michelle gellar nude movie exbyte videos new realises movies lennox movie theatre columbus oh indeo video codec free download rally music videos roots the http ejb funny video slam dunk 2005 videos three door down let me go shawshank redemption movie review mike tyson videos sitemap snoop dog doggy style movie pirate pinup girl athenian democracy history rm movies downloads movie porn sex toon jill clayburg movies movieland yonkers index site play game video poker pc mighty max license crack reagan assasination video sample movie female ejaculation medal of honor video games nbc sports video miriam gonzalez mardi gras video saturday night live celebrity jeopardy video licence plate wisconsin no leaf clover music video mixmeister 6 serial kannada movie sex long movie shot araykoo free porn searchs video imovie 3 manual site rosebud videos new york driver licences site redline movies mpeg video wizard psn stars nude movie eminem mosh music video in praise of older women movie kj52 music video video domain oasis dont look back in anger video added comment embed site video love actually movie straight monster movie vod muscle bicep video music panic video licence spysheriff real media video player link memoirs of a geisha movie poster morning latte video red dwarf movie release james bond movie trailers a common thread music video estate licensing real washington angel rap video audition top padmashree laloo prasad yadav movie webmap sitemap rudy movie posters plasmolysis video basdronda Evaluate \int _{\Gamma }{\frac  {z}{(z+2)(z-1)}}dz\, where \Gamma \, is the circle |z|=3\, traversed twice in the clockwise direction.

This is an equivalent problem:

Evaluate -2\int _{\Gamma }{\frac  {z}{(z+2)(z-1)}}dz\, where \Gamma \, is the circle |z|=3\, traversed once in the counter-clockwise direction.

The solution is 2\pi i\, times the sum of the residues of the integrand.

-2\int _{\Gamma }{\frac  {z}{(z+2)(z-1)}}dz=-2\cdot 2\pi i\left({\frac  {2}{3}}+{\frac  {1}{3}}\right)=-4\pi i\,

Main Page : Complex Variables : Complex Integrals