Calculus on Demand at Dartmouth College Lecture 20 | Index | Lecture 22
Lecture 21


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In this lecture we introduce the main ideas of integral calculus; and give an overview of the theme that unifies lectures 21-26, modeling accumulations.

Quick Question

What is the approximate area under the parabola and above the interval [0,1] that comes from using the triangle instead?



Outline for Modeling Accumulations


Modeling Accumulations

Today's Homework

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Modeling Accumulations Quiz


  • Approximate the area of an ellipse using 7 circumscribed rectangles in the first quadrant.
  • Approximate the area of the quarter circle of radius 3 centered at the origin using n circumscribed rectangles, giving your answer in terms of n.
  • The graph of a stream's rate of flow over a 1-hour period is the graph of a sine curve. Assuming the rate of flow is measured every 10 minutes, starting at time 0, use the method of accumulation to aproximate the total volume of flow over this hour, accurate to 3 decimal places.


  • Approximating Areas: Inscribed Polygons
  • Approximating Area: Using Rectangles
  • Accumulation: River Flow
  • Accumulation: Distance Traveled


  • click to see the videoWrite 1/5 + 3/25 + 5/125 + 7/625 + ... in sigma notation

Lecture 20 | Index | Lecture 22