int_{1}^{5} frac{2 cos(2x)}{x} dx, quad n = 4 (a) the Trapezoidal Rule (b) the Midpoint Rule (c) Simpson's Rule
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Since we have 4 subintervals (n=4) and the interval is from 0 to 5, the width (h) is: h = (5-0)/4 = 1.25 Now, let's evaluate the integral using each rule: (a) Trapezoidal Rule: T = (h/2) * [f(0) + 2f(1.25) + 2f(2.5) + 2f(3.75) + f(5)] T = (1.25/2) * [2cos(0) + Show more…
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