The Area Under a Curve
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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 http://online.math.uh.edu/HoustonACT/videocalculus/index.html.
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?
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Staff Review
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 studentâs 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?
This is a great review for anyone who is confused with the material towards the end of pre-calc. -
Dragonice
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.
