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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 2126, 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?
Answer
Outline
Outline for
Modeling Accumulations
Textbook
Modeling Accumulations
Today's Homework
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Quiz
Modeling Accumulations Quiz
Examples
 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 1hour 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.
Applets

Approximating Areas: Inscribed Polygons

Approximating Area: Using Rectangles

Accumulation: River Flow

Accumulation: Distance Traveled
Videos

Write 1/5 + 3/25 + 5/125 + 7/625 + ... in sigma notation
