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Graph the function .

  1. Approximate the area under the curve for using four trapezoids.

    Area of a trapezoid 

    On the given domain, what will be the height of each trapezoid?

    The bases are determined by the function.

  2. Write a Riemann sum to approximate the area under the curve for using four left endpoint rectangles. Then, use the summation feature of your graphing calculator to evaluate the sum. Compare the accuracy of the trapezoids and the rectangles.

  3. Will the approximation with trapezoids always equal the approximation with rectangles for all functions? Why or why not?

    Think about the symmetry.

Use the eTool below to visualize this problem.
Click the link at right for the full version of the eTool: Area Under a Curve eTool