Let f be the function defined by f(x)=2^(x). If three subintervals of equal length are used, what is the value of the right Riemann sum approximation for int_(1)^(2.5)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 three subintervals of equal length are used, what is the value of the right Riemann sum approximation for  int_(1)^(2.5)2^(x)dx ? Round to the nearest thousandth if necessary. Answer:

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Determine Subinterval Length: We are given the function f(x) = 2^x and we need to approximate the integral from x = 1 to x = 2.5 using a right Riemann sum with three subintervals of equal length. First, we need to determine the length of each subinterval. The total interval length is 2.5 - 1 = 1.5. Since we are using three subintervals, the length of each subinterval is 1.5 / 3 = 0.5.Find Right Endpoints: Next, we need to find the right endpoints of each subinterval. Since we start at x = 1 and each subinterval is 0.5 units long, the right endpoints will be at x = 1.5, x = 2, and x = 2.5.Evaluate Function at Endpoints: Now we evaluate the function f(x) = 2^x at each of the right endpoints. This gives us the heights of the rectangles for the Riemann sum. f(1.5) = 2^(1.5) f(2) = 2^(2) f(2.5) = 2^(2.5)Calculate Function Values: We calculate the values of the function at these points: f(1.5) = 2^(1.5) ≈ 2.8284 f(2) = 2^(2) = 4 f(2.5) = 2^(2.5) ≈ 5.6569Calculate Riemann Sum: The right Riemann sum is the sum of the areas of the rectangles. Each rectangle has a base of 0.5 (the subinterval length) and a height given by the function value at the right endpoint. So the Riemann sum is: Riemann sum ≈ 0.5 * f(1.5) + 0.5 * f(2) + 0.5 * f(2.5) Riemann sum ≈ 0.5 * 2.8284 + 0.5 * 4 + 0.5 * 5.6569Perform Calculations: Performing the calculations gives us: Riemann sum ≈ 0.5 * 2.8284 + 0.5 * 4 + 0.5 * 5.6569 Riemann sum ≈ 1.4142 + 2 + 2.8284 Riemann sum ≈ 6.2426Round to Nearest Thousandth: Rounding to the nearest thousandth, we get: Riemann sum ≈ 6.243

Let $f$ be the function defined by $f(x)=2^{x}$ . If three subintervals of equal length are used, what is the value of the right Riemann sum approximation for $\int_{1}^{2.5} 2^{x} d x$ ? Round to the nearest thousandth if necessary. $\newline$ Answer:

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Let $f$ be the function defined by $f(x)=2^{x}$ . If three subintervals of equal length are used, what is the value of the right Riemann sum approximation for $\int_{1}^{2.5} 2^{x} d x$ ? Round to the nearest thousandth if necessary. $\newline$ Answer: