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Unformatted text preview: Mathematics 1A Fall 2009 Michael Christ Lecture 32 (Monday 11/9/2009) Riemann Sums and Definition of the Definite Integral Administrative announcements: 1. Problem set 11 will be due Wednesday 11/18. 2. Wednesday 11 is Veterans Day, a campus holiday. Enjoy a well-deserved rest. 3. Todays lecture is based on 5.1 and 5.2 of our text. We will continue with 5.2 on Friday. Please read 5.2 for if you have not already done so. notation. Examples. Recall notations n , x , x i from last lecture. Sample points, and the sample point method for defining sums. The resulting sums b- a n n X i = 1 f ( x * i ) are called Riemann sums . Now we come to one of the most basic definitions of the whole course. In the following definitions, f is a function, [ a,b ] is a bounded closed interval contained in the domain of f , n is a positive integer, and for i = 0 , 2 , ,n , x i = a + i x = a + i ( b- a ) /n ....
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