Use the Midpoint Rule with n = 5 to approximate the integral. Round your answer to three decimal places.

Question

Use the Midpoint Rule with n = 5 to approximate the integral.  Round your answer to three decimal places.

Quizplus · Accepted Answer

Using the Midpoint Rule with n = 5 gives:
Δx = (2-0)/5 = 0.4
x1 = 0.2, x2 = 0.6, x3 = 1, x4 = 1.4, x5 = 1.8
f(x1) = e^(0.2) ≈ 1.221
f(x2) = e^(0.6) ≈ 1.822
f(x3) = e^(1) ≈ 2.718
f(x4) = e^(1.4) ≈ 4.055
f(x5) = e^(1.8) ≈ 6.049
Using the Midpoint Rule formula:
∫₀² e^x dx ≈ Δx [f(x1) + f(x2) + f(x3) + f(x4) + f(x5)]
≈ 0.4 [1.221 + 1.822 + 2.718 + 4.055 + 6.049]
≈ 5.693
Rounded to three decimal places, the answer is 5.693, which corresponds to choice C.

Use the Midpoint Rule with N = 5 to Approximate