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 Area Under a Curve Subject Area: Pre-Calculus or Calculus Grade Level: 11 - 12 National Mathematics Standard: Investigate the area under a curve and the rate of change. National Technology Standards: Technology research tools: Use content-specific tools, software and simulations (e.g., environmental probes, graphing calculators, exploratory environments, Web tools) to support learning and research; select and use appropriate tools and technology resources to accomplish a variety of tasks and solve problems. Problem-Solving and Decision-Making Tools - Routinely and efficiently use on-line information resources to meet needs for collaboration, research, publications, communications, and productivity. Objectives: Use the idea of area between curves to make inferences about the forces of pressure on the wing area of an airplane given altitude changes. FoilSim is an interactive simulation software package that examines the airflow around various shapes of airfoils. As you change parameters such as airspeed, altitude, angle of attack, thickness and curvature of the airfoil, and size of the wing area, the software calculates the lift. The package was created at the NASA Glenn Research Center. FoilSim II is a Java applet program that executes inside the browser of your computer. It is available on the World Wide Web at http://www.grc.nasa.gov/WWW/K-12/airplane/foil2.html. You can also download the program to run off-line. Shown below is a screen shot from the program's controls and displays. You may change the values of the variables by using the slider or the input box on the left of the slider. To use the slider: Click the mouse pointer on the arrows at the ends of the slider. Click the mouse pointer anywhere between the slider and the arrow. Drag the slider with the mouse. To use the input box: Simply select the value in the input box, key in the new value, and press Enter or Tab when finished. The button on the slider will move corresponding to the value typed in the box. To begin the activity, click on the Area Under a Curve Activity.   Assessment: You, as individuals or in cooperative groups, will be evaluated on: The feasibility of your answers. Your explanations for given questions. Evaluation: You will be evaluated on the graphs created and their comparison to the graphs in FoilSim. Submitted by: Christine Nagy Warren, Olmsted Falls High School, Olmsted Falls, Ohio.

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