Let f be the function defined by f(x)=4sqrtx. If three subintervals of equal length are used, what is the value of the trapezoidal sum approximation for int_(3)^(4.5)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 trapezoidal sum approximation for  int_(3)^(4.5)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 from 3 to 4.5 has a length of 4.5 - 3 = 1.5. Since we are using three subintervals, each subinterval will have a width of 1.5 / 3 = 0.5.Calculate Function Values: Next, we need to calculate the values of the function f(x) = 4√x at the endpoints of each subinterval. These points are x = 3, x = 3.5, x = 4, and x = 4.5. We will calculate f(x) for each of these x-values.Apply Trapezoidal Rule: f(3) = 4√3 ≈ 4 * 1.732 = 6.928 f(3.5) = 4√3.5 ≈ 4 * 1.871 = 7.484 f(4) = 4√4 = 4 * 2 = 8 f(4.5) = 4√4.5 ≈ 4 * 2.121 = 8.484Plug in Values: Now we apply the trapezoidal rule, which is given by the formula: T = (width/2) * (f(a) + 2*f(a+width) + 2*f(a+2*width) + ... + f(b)) where a and b are the start and end points of the interval, and width is the width of each subinterval.Perform Calculations: Plugging in the values we have: T = (0.5/2) * (f(3) + 2*f(3.5) + 2*f(4) + f(4.5)) T = (0.25) * (6.928 + 2*7.484 + 2*8 + 8.484)Round the Result: Now we perform the calculations: T = (0.25) * (6.928 + 14.968 + 16 + 8.484) T = (0.25) * (46.38) T ≈ 11.595We round the result to the nearest thousandth as instructed: T ≈ 11.595

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 trapezoidal sum approximation for $\int_{3}^{4.5} 4 \sqrt{x} d x$ ? Round to the nearest thousandth if necessary. $\newline$ Answer:

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