Write the Riemann sum that would approximate the area of the following graph over the interval [0,3] using 3 subintervals.

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Identify the function given in the graph, which is $ f(x) = x^3 - 3x + 2 $.

Determine the interval over which we need to approximate the area, which is [0, 3].

Divide the interval [0, 3] into 3 equal subintervals. Each subinterval will have a width of $ \Delta x = \frac{3 - 0}{3} = 1 $.

Choose the sample points for each subinterval. For simplicity, we can use the left endpoints: $ x_0 = 0 $, $ x_1 = 1 $, and $ x_2 = 2 $.

Write the Riemann sum using the left endpoints: $ R = f(x_0) \cdot \Delta x + f(x_1) \cdot \Delta x + f(x_2) \cdot \Delta x $. Substitute the function values: $ R = (f(0) + f(1) + f(2)) \cdot 1 $.

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객관식

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