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# Integrals : Lower Riemann Sum

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21. The region S is bounded by y = x2 - 2x + 3, y = 0, x = 0, and x = 9. Which of the following is the approximation to the area of S obtained by computing the sum of the areas of the 3 inscribed rectangles with bases [0,3], [3,6], and [6,9] (lower Riemann sum)?
A. 105 B. 108 C. 117
D. 189 E. 297

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#### Solution Preview

The parabola y = x2 - 2x + 3 has a minimum of y = 2 at x = 1 (see the graph below). Thus the three inscribed rectangles have heights of 2, 6, and 27 respectively. Since each has a base of length 3 the Riemann ...

#### Solution Summary

A lower Riemann sum is found. The response received a rating of "5" from the student who posted the question.

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