Math1011_Week14 - Math1011 Section 5.4 Evaluate the...

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Math1011 Section 5.4 11/22/2010 Evaluate the following definite integrals using an antiderivative. 2 0 (3 2) + x dx 1 2 (3 2) x dx + 2 2 / 4 1 cos cos 0 x x dx π +
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Math1011 Section 5.4 1 Evaluate the integrals 2 0 (3 2) + x dx 2 2 2 2 2 0 (2) (0) 2 2 3 2 3 2(2) 3 2(0) 6 4 x x + + + = + = 10 1 2 (3 2) + x dx [ ] [ ] 2 2 2 1 2 2 ( 1) ( 2) 3 5 2 2 2 3 2 3 2( 1) 3 2( 2) 2 6 4 x x + + + = = − 2 2 2 / 4 1 cos cos 0 x x dx π + ] 2 2 2 / 4 cos 1 cos cos 0 / 4 2 0 / 4 0 4 4 4 4 sec 1 tan (tan ) (tan0 0) (1 ) (0 0) 1 x x x dx x dx x x π π π π π π + + + + + = + + = + π Evaluation Theorem If ƒ is continuous on the interval [a, b], then ( ) ( ) ( ) b a f x dx F b F a = where F is any antiderivative of ƒ, that is F’=ƒ. (Doc #1011w.54.01)
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