If f(x) = ex − 1, 0 ≤ x ≤ 2, find the riemann sum with n = 4 correct to six decimal places, taking the sample points to be midpoints.

Since 0 < x < 2 and n = 4 we see that each sub interval is of lenght (b - a)/n = (2 - 0)/4 = 1/2 [0, 1/2] [1/2, 1] [1, 3/2] [3/2, 2] The midpoints are t0 = 1/4, t1 = 3/4, t2 = 5/4, and t3 = 7/4 Riemann sum is Sum from i = 0 to 3 {f(ti) * (b-a)/n} Sum from i = 0 to 3 {(e^(ti) - 5) * 1/2} (1/2) Sum from i = 0 to 3 {e^(ti) - 5} (1/2) [e^(t0) - 5 + e^(t1) - 5 + e^(t2) - 5 + e^(t3) - 5] (1/2) [e^(1/4) + e^(3/4) + e^(5/4) + e^(7/4) - 20]

The answer to your question is 1/9