Let f be the function defined by f(x)=4sqrtx. If three subintervals of equal length are used, what is the value of the right Riemann sum approximation for int_(0)^(9)4sqrtxdx ? Round to the nearest thousandth if necessary. Answer:

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Let  f be the function defined by  f(x)=4sqrtx. If three subintervals of equal length are used, what is the value of the right Riemann sum approximation for  int_(0)^(9)4sqrtxdx ? Round to the nearest thousandth if necessary. Answer:

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Determine Subinterval Length: To approximate the integral of f(x) = 4√x from 0 to 9 using a right Riemann sum with three subintervals of equal length, we first need to determine the length of each subinterval. The interval [0, 9] is divided into three equal parts, so each subinterval has a length of 9/3 = 3.Find Right Endpoints: Next, we need to find the right endpoints of each subinterval. Since we are using a right Riemann sum, we will evaluate the function at these right endpoints. The right endpoints are x = 3, x = 6, and x = 9.Evaluate Function at Endpoints: Now we evaluate the function f(x) = 4√x at each of the right endpoints. This gives us f(3) = 4√3, f(6) = 4√6, and f(9) = 4√9.Calculate Function Values: We calculate the values: f(3) = 4√3 ≈ 4 * 1.732 = 6.928, f(6) = 4√6 ≈ 4 * 2.449 = 9.796, and f(9) = 4√9 = 4 * 3 = 12.Calculate Riemann Sum: The right Riemann sum is the sum of the products of the function values at the right endpoints and the length of each subinterval. So, the right Riemann sum R is R = (f(3) + f(6) + f(9)) * length of subinterval.Substitute Values: Substitute the values we found into the Riemann sum formula: R = (6.928 + 9.796 + 12) * 3.Perform Calculation: Perform the calculation: R = (6.928 + 9.796 + 12) * 3 ≈ 28.724 * 3 ≈ 86.172.Round Result: Round the result to the nearest thousandth: R ≈ 86.172.

Let $f$ be the function defined by $f(x)=4 \sqrt{x}$ . If three subintervals of equal length are used, what is the value of the right Riemann sum approximation for $\int_{0}^{9} 4 \sqrt{x} d x$ ? Round to the nearest thousandth if necessary. $\newline$ Answer:

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Let $f$ be the function defined by $f(x)=4 \sqrt{x}$ . If three subintervals of equal length are used, what is the value of the right Riemann sum approximation for $\int_{0}^{9} 4 \sqrt{x} d x$ ? Round to the nearest thousandth if necessary. $\newline$ Answer: