1 / 7

Applied Calculus (MAT 121) Dr. Day Wednesday, March 28, 2012

Applied Calculus (MAT 121) Dr. Day Wednesday, March 28, 2012. Calculating Antiderivatives (6.1 ) and Area Under a Curve ( 6.3). Integration. Big Ideas What is an antiderivative , how do we determine one, and how do we represent it with symbols?

tan
Download Presentation

Applied Calculus (MAT 121) Dr. Day Wednesday, March 28, 2012

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Applied Calculus (MAT 121)Dr. Day Wednesday, March 28, 2012 Calculating Antiderivatives (6.1) and Area Under a Curve (6.3) MAT 121

  2. 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. MAT 121

  3. 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. MAT 121

  4. 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 + 50. 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. MAT 121

  5. 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. MAT 121

  6. Approximating Area: Riemann Sums Riemann Sum Applet MAT 121

  7. Assignments WebAssign 6.1 due tonight 6.3 due tomorrow night Test #4: Check your scores, look for errors, revisit every problem you missed! MAT 121

More Related