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Midpoint rectangles have their height defined at the midpoint of the interval. For the function

graphed at right, you previously found the heights to be .

  1. Approximate the area under the curve for using midpoint rectangles.

    There are only three rectangles.
    No need to use sigma notation.

    Just find the area of each rectangle and add. Be sure to organize your work in a way that others will understand your process.

  2. Calculate the exact area and compare it with your approximation.

    Find the exact area using a definite integral.