intregrals - Integrals General Integration Rules b a b a...

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Integrals General Integration Rules = b a a b c cdx ) ( ∫∫ + = + b a b a b a dx x g dx x f dx x g x f ) ( ) ( )] ( ) ( [ = b a b a b a dx x g dx x f dx x g x f ) ( ) ( )] ( ) ( [ = + b a b c c a dx x f dx x f dx x f ) ( ) ( ) ( Comparison Properties of Integrals If for a , then . 0 ) ( x f b x b a dx x f 0 ) ( If ) ( ) ( x g x f for a , then . b x b a b a dx x g dx x f ) ( ) ( If M x f m ) ( for a b x , then . ) ( ) ( ) ( a b M dx x f a b m b a The Fundamental Theorem Of Calculus Suppose f is continuous on [a,b] 1. , then g’(x)=f(x). = x a dt t f x g ) ( ) ( 2. , where F is any antiderivative of f, that is, F’=f. = b a a F b F dx x f ) ( ) ( ) ( Table of Integrals = dx x f c dx x cf ) ( ) ( C kx kxdx + = ) 1 ( , 1 1
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