2311lectureoutline5.1 - the height is determined by the...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
MAC2311, Calculus I 5.1 Areas To approximate the area under a curve, we can approximate the region by using rectangles and letting the number of rectangles become large. The precise area is the limit of these sums of areas of rectangles. A right sum, R n , is the sum of the area of rectangles under the curve f(x) where x Δ is the width of each rectangle and f(x i ) is the height of each rectangle, where the height is determined by the right side of the rectangle touching the curve. A left sum, L n , is the sum of the area of rectangles under the curve f(x) where x Δ is the width of each rectangle and f(x i ) is the height of each rectangle, where
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: the height is determined by the left side of the rectangle touching the curve. Definition: Let a function f be defined on the interval [a, b] and let f(x)> 0 for all x in [a,b]. Then the area A of the region that lies between the graph of f and the x-axis is the limit of the sum of the areas of approximating rectangles: 1 2 1 [ ( ) ( ) ... ( ) ] lim lim lim ( ) n n n i i n n n i A R f x x f x x f x x f x x →∞ →∞ →∞ = = = Δ + Δ + + Δ = Δ & where b a x n-Δ = and i x a i x = + Δ , provided the limit exists. Try exercises 2, 4, 18, 24 on pages 364-365 in your text....
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