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First quadrant, x axis scaled from 0 to 4, curve coming from lower left through the point (0, comma 1), turning at approximate points (0.5, comma 1.2) & (2.5, comma 0.5), 3 vertical bars, bottom edges on x axis, each with width, 1, starting at, x = 1, & each with midpoint of top edge, on the curve.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  and .

  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.