Let f be the function defined by f(x)=2^(x). If six subintervals of equal length are used, what is the value of the right Riemann sum approximation for int_(2)^(3.5)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 six subintervals of equal length are used, what is the value of the right Riemann sum approximation for  int_(2)^(3.5)2^(x)dx ? Round to the nearest thousandth if necessary. Answer:

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Determine subinterval width: Determine the width of each subinterval. The interval [2, 3.5] has a length of 3.5 - 2 = 1.5. Since we are using six subintervals of equal length, the width (Δx) of each subinterval is 1.5/6.Calculate width: Calculate the width of each subinterval. Δx = 1.5/6 = 0.25.Identify right endpoints: Identify the x-values for the right endpoints of each subinterval. Since we are using right Riemann sums, we need the x-values at the right endpoints of each subinterval. Starting from x = 2 and adding the width of each subinterval, we get the following x-values: 2.25, 2.5, 2.75, 3, 3.25, and 3.5.Evaluate function at endpoints: Evaluate the function f(x) = 2^x at each of the right endpoints. f(2.25) = 2^(2.25) f(2.5) = 2^(2.5) f(2.75) = 2^(2.75) f(3) = 2^(3) f(3.25) = 2^(3.25) f(3.5) = 2^(3.5)Calculate Riemann sum: Calculate the right Riemann sum approximation. Right Riemann sum = Δx * (f(2.25) + f(2.5) + f(2.75) + f(3) + f(3.25) + f(3.5)) = 0.25 * (2^(2.25) + 2^(2.5) + 2^(2.75) + 2^(3) + 2^(3.25) + 2^(3.5))Perform sum calculations: Perform the calculations to find the sum. Right Riemann sum = 0.25 * (5.656854249 + 5.656854249 + 6.349604208 + 8 + 9.189586844 + 11.3137085) = 0.25 * (46.16660805) = 11.54165201Round to nearest thousandth: Round the result to the nearest thousandth. Right Riemann sum ≈ 11.542

Let $f$ be the function defined by $f(x)=2^{x}$ . If six subintervals of equal length are used, what is the value of the right Riemann sum approximation for $\int_{2}^{3.5} 2^{x} d x$ ? 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 six subintervals of equal length are used, what is the value of the right Riemann sum approximation for $\int_{2}^{3.5} 2^{x} d x$ ? Round to the nearest thousandth if necessary. $\newline$ Answer: