With the tie effectively over after West Ham's leaky defence shipped six goals in the first leg two weeks ago, City dished out an extra helping of humiliation with Alvaro Negredo scoring twice and Sergio Aguero also netting.
City will face either Sunderland or local rivals Manchester United in the final on March 2, with Sunderland holding a slender 2-1 advantage heading into the second leg on Wednesday.
(Reporting by Toby Davis; editing by Martyn Herman)
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