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Applied Calculus (MAT 121) Dr. Day Wednesday, March 28, 2012
Calculating Antiderivatives (6.1) and Area Under a Curve (6.3) Wednesday, March 28, 2012 MAT 121
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Integration Big Ideas What is an antiderivative, how do we determine one, and how do we represent it with symbols? How can we determine the area under a curve or trapped between two curves, and how does the integral relate to that? The definite integral of a rate function gives use an accumulation. The Fundamental Theorem of Calculus: Connecting derivatives and integrals. Wednesday, March 28, 2012 MAT 121
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Antiderivatives, Integrals, and Initial Value Problems
Knowing f’, can we determine f ? General and specific solutions: The antiderivative. The integral symbol: Representing antiderivatives Initial Value Problems: Transforming a general antiderivative into a specific function that satisfies the given information. Wednesday, March 28, 2012 MAT 121
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If we know a rate function . . .
Carlota Music Company estimates that the marginal cost of manufacturing its Professional Series guitars is given by the following in dollars/month when the level of production is x guitars/month: C '(x) = 0.004x The fixed costs incurred by Carlota are $9000/month. Determine a model for the total monthly cost C(x) incurred by Carlota in manufacturing x guitars/month. Wednesday, March 28, 2012 MAT 121
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Approximating Area: Riemann Sums
To generate a way to calculate the area under the curve of a rate function, in order to determine an accumulation, we begin with AREA APPROXIMATIONS. We create something called a Riemann Sum and use better and better area approximations that will lead to exact area. Wednesday, March 28, 2012 MAT 121
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Approximating Area: Riemann Sums
Riemann Sum Applet Wednesday, March 28, 2012 MAT 121
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Assignments WebAssign 6.1 due tonight 6.3 due tomorrow night Test #4: Check your scores, look for errors, revisit every problem you missed! Wednesday, March 28, 2012 MAT 121
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