# 1-5 - January 5 2005 Announcements You need to have...

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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.) Always bring this to your Tu & Th sections. All the problems from the book Calculus, Early Transcendentals by James Stewart, 5th Edition can be found at 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.
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 + Δ x for 0 ≤ k ≤ n-1 Compute R n and L n : R n = f ( x 1 )Δ x + f ( x 2 )Δ x + ··· + f ( x n )Δ x L n = f ( x )Δ x + f ( x 1 )Δ x + ··· + f ( x n-1 )Δ x Deﬁnition. 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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• Spring '08
• varies
• Calculus, non-negative continuous function

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