Let f be the function defined by f(x)=x^(2). If four subintervals of equal length are used, what is the value of the trapezoidal sum approximation for int_(2)^(3)x^(2)dx ? Round to the nearest thousandth if necessary. Answer:

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Let  f be the function defined by  f(x)=x^(2). If four subintervals of equal length are used, what is the value of the trapezoidal sum approximation for  int_(2)^(3)x^(2)dx ? 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 from 2 to 3 has a length of 1. Since we are using four subintervals, each subinterval will have a width of 1/4. Calculation: (3 - 2) / 4 = 1/4Calculate Function Values: Next, we need to calculate the values of the function f(x) = x^2 at the endpoints of each subinterval. These points are x = 2, x = 2.25, x = 2.5, x = 2.75, and x = 3. Calculation: f(2) = 2^2 = 4, f(2.25) = 2.25^2 = 5.0625, f(2.5) = 2.5^2 = 6.25, f(2.75) = 2.75^2 = 7.5625, f(3) = 3^2 = 9Apply Trapezoidal Rule: Now we apply the trapezoidal rule, which is given by the formula: Trapezoidal Sum = (width/2) * (f(x_0) + 2*f(x_1) + 2*f(x_2) + 2*f(x_3) + f(x_4)) where x_0, x_1, x_2, x_3, and x_4 are the endpoints of the subintervals.Plug in Values: Plugging in the values we have: Trapezoidal Sum = (1/4/2) * (f(2) + 2*f(2.25) + 2*f(2.5) + 2*f(2.75) + f(3)) Trapezoidal Sum = (1/8) * (4 + 2*5.0625 + 2*6.25 + 2*7.5625 + 9)Perform Calculations: Performing the calculations: Trapezoidal Sum = (1/8) * (4 + 10.125 + 12.5 + 15.125 + 9) Trapezoidal Sum = (1/8) * 50.75 Trapezoidal Sum = 6.34375Round to Nearest Thousandth: Rounding to the nearest thousandth, we get: Trapezoidal Sum ≈ 6.344

Let $f$ be the function defined by $f(x)=x^{2}$ . If four subintervals of equal length are used, what is the value of the trapezoidal sum approximation for $\int_{2}^{3} x^{2} d x$ ? Round to the nearest thousandth if necessary. $\newline$ Answer:

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Let $f$ be the function defined by $f(x)=x^{2}$ . If four subintervals of equal length are used, what is the value of the trapezoidal sum approximation for $\int_{2}^{3} x^{2} d x$ ? Round to the nearest thousandth if necessary. $\newline$ Answer: