5. The table below gives data points for a continuous function f on [2, 10]. x | 2 | 5 | 7 | 8 | 10 f(x) | 3 | 1 | 5 | 3 | 5 Using subdivisions [2, 5], [5, 8] and [8, 10], what is the trapezoid approximation of integral from 2 to 10 of f(x) dx? (A) 18 (B) 20 (C) 22 (D) 24 (E) 40
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Step 1:** Calculate the trapezoid approximation using the formula: \[ \text{Trapezoid Approximation} = \frac{\Delta x_1}{2} \times (f(2) + f(5)) + \frac{\Delta x_2}{2} \times (f(5) + f(8)) + \frac{\Delta x_3}{2} \times (f(8) + f(10)) \] ** Show more…
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