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Unformatted text preview: Math Camp Notes: Integration I De nite Integrals Consider a function f ( x ) . The area under the graph of the function between points x = a and x = b is denoted by R b a f ( x ) dx , and is called the de nite integral of f ( x ) between a and b . If f ( t ) and g ( t ) are integrable functions, then the following properties of the de nite integral hold: 1. R b a [ f ( t ) + g ( t )] dt = R b a f ( t ) dt + R b a g ( t ) dt 2. R b a λf ( t ) dt = λ R b a f ( t ) dt 3. R c a f ( t ) dt = R b a f ( t ) dt + R c b f ( t ) dt 4. R b a f ( t ) dt =- R a b f ( t ) dt 5. R a a f ( t ) dt = 0 Inde nite Integrals If f ( x ) is given then any function F ( x ) such that F ( x ) = f ( x ) is called an inde nite integral of f ( x ) , or the anti-derivative. Note that there are in nitely many anti-derivatives of a function f ( x ) since they can di er by a constant. We denote the anti-derivative by R f ( x ) dx . The following are some simple rules for nding anti-derivatives: 1. R x n dx = x n +1 n +1 + C 2....
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This note was uploaded on 09/20/2010 for the course AMATH 351 taught by Professor Sivabalsivaloganathan during the Spring '08 term at Waterloo.
- Spring '08