1-5 - a, b ] into n subintervals: [ x , x 1 ] , [ x 1 , x 2...

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January 5, 2005 Announcements You need to have the “Math 125 course pak”. ($8.50 from the UW Copy Center in Communications (CMU) B042.) All the problems from the book Calculus, Early Transcendentals by James Stewart, 5th Edition can be found at http://www.math.washington.edu/˜m124/ Stewart5Eprobs/ 1
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Today: § 5.1: Areas and Distances Area problem: Find the area of a region that lies under a curve. Turn an intuitive idea of area into a precise math- ematical definition. Distance problem.
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Area Problem: Find the area of the region S bounded by the graph of a non-negative continuous function f , the x -axis and the vertical lines x = a and x = b . S = { ( x, y ) : a x b, 0 y f ( x ) }
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Idea: Divide S into n strips of the same width, Δ x = b - a n There is a corresponding division of [
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Unformatted text preview: a, b ] into n subintervals: [ x , x 1 ] , [ x 1 , x 2 ] , , [ x n-1 , x n ] where x = a, x n = b, x k +1 = x k + x for 0 k n-1 Compute R n and L n : R n = f ( x 1 ) x + f ( x 2 ) x + + f ( x n ) x L n = f ( x ) x + f ( x 1 ) x + + f ( x n-1 ) x Denition. The area of the region S bounded by the graph of a non-negative continuous func-tion f , the x-axis and the vertical lines x = a and x = b is A = lim n R n = lim n L n . The velocity graph of a car accelerating from rest to a speed of 120 km/h over a period of 30 seconds is shown. Estimate the distance traveled during this period.-6 v (km/h) 80 40 10 20 30 t (seconds)...
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1-5 - a, b ] into n subintervals: [ x , x 1 ] , [ x 1 , x 2...

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