Let f be the function defined by f(x)=(2)/(x). If five subintervals of equal length are used, what is the value of the right Riemann sum approximation for int_(1)^(6)(2)/(x)dx ? Round to the nearest thousandth if necessary. Answer:

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Let  f be the function defined by  f(x)=(2)/(x). If five subintervals of equal length are used, what is the value of the right Riemann sum approximation for  int_(1)^(6)(2)/(x)dx ? Round to the nearest thousandth if necessary. Answer:

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Determine Subinterval Width: We are given the function f(x) = 2/x and we need to approximate the integral from x = 1 to x = 6 using a right Riemann sum with five subintervals of equal length. The first step is to determine the width of each subinterval. The total interval length is 6 - 1 = 5. Since we are using five subintervals, the width of each subinterval (Δx) is 5/5 = 1.Find Evaluation Points: Next, we need to find the x-values at which we will evaluate the function for the right Riemann sum. Since we are using the right endpoints and the first subinterval starts at x = 1, the x-values will be 2, 3, 4, 5, and 6.Evaluate Function: Now we evaluate the function f(x) = 2/x at each of these x-values: f(2) = 2/2 = 1 f(3) = 2/3 ≈ 0.667 f(4) = 2/4 = 0.5 f(5) = 2/5 = 0.4 f(6) = 2/6 ≈ 0.333Calculate Rectangle Areas: We then multiply each function value by the width of the subintervals (Δx = 1) to get the area of each rectangle in the Riemann sum: Area at x=2: 1 * Δx = 1 * 1 = 1 Area at x=3: 0.667 * Δx = 0.667 * 1 ≈ 0.667 Area at x=4: 0.5 * Δx = 0.5 * 1 = 0.5 Area at x=5: 0.4 * Δx = 0.4 * 1 = 0.4 Area at x=6: 0.333 * Δx = 0.333 * 1 ≈ 0.333Sum Rectangle Areas: Finally, we sum the areas of all the rectangles to get the right Riemann sum approximation for the integral: Right Riemann sum = 1 + 0.667 + 0.5 + 0.4 + 0.333 ≈ 2.9Round Final Result: We round the result to the nearest thousandth as instructed: Right Riemann sum ≈ 2.900

Let $f$ be the function defined by $f(x)=\frac{2}{x}$ . If five subintervals of equal length are used, what is the value of the right Riemann sum approximation for $\int_{1}^{6} \frac{2}{x} d x$ ? Round to the nearest thousandth if necessary. $\newline$ Answer:

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Let $f$ be the function defined by $f(x)=\frac{2}{x}$ . If five subintervals of equal length are used, what is the value of the right Riemann sum approximation for $\int_{1}^{6} \frac{2}{x} d x$ ? Round to the nearest thousandth if necessary. $\newline$ Answer: