1-5 - a b into n subintervals x x 1 x 1 x 2 ·· x n-1 x n...

Info icon This preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
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 http://www.math.washington.edu/˜m124/ Stewart5Eprobs/ 1
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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.
Image of page 2
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 ) }
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Idea: Divide S into n strips of the same width, Δ x = b - a n There is a corresponding division of [
Image of page 4
Image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

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)...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern