Let f be the function defined by f(x)=4sqrtx. If four subintervals of equal length are used, what is the value of the trapezoidal sum approximation for int_(1)^(7)4sqrtxdx ? Round to the nearest thousandth if necessary. Answer:

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Let  f be the function defined by  f(x)=4sqrtx. If four subintervals of equal length are used, what is the value of the trapezoidal sum approximation for  int_(1)^(7)4sqrtxdx ? Round to the nearest thousandth if necessary. Answer:

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Determine Subinterval Width: To use the trapezoidal rule, we first need to determine the width of each subinterval. The interval [1, 7] has a length of 7 - 1 = 6. Since we are using four subintervals, each subinterval will have a width of 6 / 4 = 1.5.Calculate Function Values: Next, we need to calculate the values of the function f(x) = 4√x at the endpoints of each subinterval. The endpoints are x = 1, x = 2.5, x = 4, x = 5.5, and x = 7. We will calculate f(x) for each of these x-values.Apply Trapezoidal Rule: f(1) = 4√1 = 4(1) = 4 f(2.5) = 4√2.5 ≈ 4(1.581) ≈ 6.324 f(4) = 4√4 = 4(2) = 8 f(5.5) = 4√5.5 ≈ 4(2.345) ≈ 9.38 f(7) = 4√7 ≈ 4(2.646) ≈ 10.584Plug in Values: Now we apply the trapezoidal rule, which is given by the formula: T = (width/2) * (f(x_0) + 2f(x_1) + 2f(x_2) + ... + 2f(x_{n-1}) + f(x_n)) where x_0, x_1, ..., x_n are the endpoints of the subintervals and n is the number of subintervals.Perform Calculations: Plugging in the values we have: T = (1.5/2) * (f(1) + 2f(2.5) + 2f(4) + 2f(5.5) + f(7)) T = (0.75) * (4 + 2(6.324) + 2(8) + 2(9.38) + 10.584)Round to Nearest Thousandth: Now we perform the calculations: T = 0.75 * (4 + 12.648 + 16 + 18.76 + 10.584) T = 0.75 * (61.992) T ≈ 46.494Rounding to the nearest thousandth, we get: T ≈ 46.494

Let $f$ be the function defined by $f(x)=4 \sqrt{x}$ . If four subintervals of equal length are used, what is the value of the trapezoidal sum approximation for $\int_{1}^{7} 4 \sqrt{x} d x$ ? 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 four subintervals of equal length are used, what is the value of the trapezoidal sum approximation for $\int_{1}^{7} 4 \sqrt{x} d x$ ? Round to the nearest thousandth if necessary. $\newline$ Answer: