Question: Use a Riemann sum with n = 5 and midpoints to estimate the area under the graph of f (x) = 1 - x 2

Use a Riemann sum with n = 5 and midpoints to estimate the area under the graph of f (x) = √1 - x² on the interval 0 ≤ x ≤ 1. The graph is a quarter circle, and the area under the graph is .78540, to five decimal places. See Fig. 16. Carry out the calculations to five decimal places and compute the error. 1 y y=1-x 0 Figure 16 1 X

1 y y=1-x 0 Figure 16 1 X

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