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March 8HWK #6 due R 3/15 or F 3/167.1: 10, 16, 24, 33, 36, 397.2: 10, 14, 18, 24, 32, 34Spring Break March 17-25Prelim 2: Thursday March 29Covers up to and including 7.2.IntegrationIf F′(x) = f(x) then F is an antiderivativeof f.Fact. If F and G are antiderivatives of f then F-G is a constant.If f(t) is velocity at time t, then F(t) is position. From velocity we can only determine position up to a constant F(0).Indefinite integralIf '( )( ) then we write( )( )Fxf xf x dxF xC==+∫We say F is the indefinite integralof f. This is just another word for antiderivative.+C reminds us that one we have one antiderivative we get all the others by adding a constant.Integration Formula 111(1)when 11I1. 11pppppdxpxxpxx dxCpdx pp+++==≠+=−+++∫Problem1523Find the antiderivative of26711ppxx dxCxxxpxp+=+≠ −++++∫Solution52521/233633/221Find the antiderivative of2I don't wri11te th676727233e +Cppxxxxxxxxxxx dxCxxppx+−−+++=+++++=+−+−≠∫
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