For each problem, approximate the area under the curve over the given interval using 4 midpoint rectangles. 7) y = x 2 2- x + 1; [-3, 5]

Question

Midpoint Reimann Sum Problem

Answer 1

f(x) = x² - x + 1

Divide the interval [-3,5] into 4 intervals each of width Δx = (5 - (-3)) / 4 = 2

First interval: [-3, -1] with midpoint -2

Second interval: [-1, 1] with midpoint 0

Third interval: [1, 3} with midpoint 2

Fourth interval: [3, 5] with midpoint 4

Midpoint Riemann Sum = f(-2)Δx + f(0)Δx + f(2)Δx + f(4)Δx = 2[7 + 1 + 3 + 13] = 48