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This Exploration uses the interactive Java applet MIC AreaGrapher (below) to find the area under graphs, as referenced on page 13-11 of your text.
Instructions
- Please be patient while the program is loading. It can take up to 30 seconds to load and then run, depending on the available bandwidth. It runs much faster if you download it to your hard drive.
- In the box following "f(x) = " enter the equation "3*x^2" and check the box to its immediate right.
- Change the axes to read XMin = -3.5, XMax = 3.5, XScl = 1, YMin = -5, YMax = 8, Scl = 10, and make the bounds Lower = -3, Upper = 3
- Click the "Graph" button.
- The graph of f(x) will be drawn (in red)
- Using the mouse, click anywhere along the x-axis between the bounds. The area will be shaded between f(x) and the x-axis and the value for the area will be shown. Also a blue dot representing this value for area will be placed on the grid. If you want the area between the bounds, click anywhere to the right of the upper bound.
- Continue clicking under the curve until the shape of the accumulated area function becomes apparent.
- Try to determine the equation for the accumulated area function, and enter it in the box beside "A(x) =" and check the box to its immediate right. The graph of your equation will be drawn in magenta. Click along the x-axis to see if the line "fits" the points.
- Does the accumulated area function "fit" the points? If so then A(x) must be the correct function. If not, adjust you equation for A(x).
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