The Area Under a Curve

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Taught by Houston
  • Currently 4.0/5 Stars.
6851 views | 3 ratings
Meets NCTM Standards:
Features a TI Calculator
Lesson Description:

Approximation of areas with sums of rectangle areas. Right-endpoint, left-endpoint, and midpoint approximations; upper and lower sums.

Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more information on videos, resources, and lessons at

Questions answered by this video:
  • How do you find the area under a curve?
  • How do you use rectangles to find the area under a curve?
  • What is left-endpoint, right-endpoint, and midpoint approximation of area under a curve using rectangles?
  • How do you approximate the area under a curve with rectangles using a graphing calculator?
  • What are inscribed and circumscribed rectangles?
  • What are lower and upper sums of the area under a curve?
  • How do you find the exact area under a curve?
  • Staff Review

    • Currently 4.0/5 Stars.
    This video explains very clearly and precisely one of the most important topics in Calculus: the area under a curve. It starts out with approximating using rectangle areas at a very theoretical and high level. Some of the terminology and notation is above a beginning Calculus student’s level. Some concrete examples are also used, however, which are more accessible to the majority of students. You will also learn how to find these sums on a graphing calculator. In the end, the video leads up to finding the exact area under a curve by finding the integral.
  • IlikePi?

    • Currently 4.0/5 Stars.
    This is a great review for anyone who is confused with the material towards the end of pre-calc.
  • Dragonice

    • Currently 5.0/5 Stars.
    WOW, I actually understand this now! Thanks a lot. The calculus book I have and my teacher made it seem too complicated. Thanks for going step by step.