Integrals General Integration Rules ∫−=baabccdx)(∫∫+∫=+bababadxxgdxxfdxxgxf)()()]()([−∫=−bababadxxgdxxfdxxgxf)()()]()([∫=∫+∫babccadxxfdxxfdxxf)()()(Comparison Properties of IntegralsIf for a, then . 0)(≥xfbx≤≤∫≥badxxf0)(If )()(xgxf≥for a, then . bx≤≤∫≥∫babadxxgdxxf)()(If Mxfm≤≤)(for abx≤≤, then . )()()(abMdxxfabmba−≤∫≤−The Fundamental Theorem Of CalculusSuppose f is continuous on [a,b] 1. , then g’(x)=f(x). ∫=xadttfxg)()(2. , where F is any antiderivative of f, that is, F’=f. ∫−=baaFbFdxxf)()()(Table of Integrals∫=∫dxxfcdxxcf)()(Ckxkxdx+=∫)1(,11−≠
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This note was uploaded on 05/01/2008 for the course CALC 205 taught by Professor Hu during the Spring '08 term at University of Louisville.