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 right Riemann sum approximation for int_(2)^(6)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 right Riemann sum approximation for  int_(2)^(6)x^(2)dx ? Round to the nearest thousandth if necessary. Answer:

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Determine Width of Subintervals: Determine the width of each subinterval. Since we are integrating from x = 2 to x = 6, the total interval length is 6 - 2 = 4. With four subintervals of equal length, each subinterval will have a width of 4 / 4 = 1.Identify Endpoints of Subintervals: Identify the endpoints of each subinterval. The subintervals are [2, 3], [3, 4], [4, 5], and [5, 6]. Since we are using a right Riemann sum, we will evaluate the function at the right endpoints of each subinterval, which are x = 3, x = 4, x = 5, and x = 6.Evaluate Function at Endpoints: Evaluate the function at each right endpoint. f(3) = 3^2 = 9 f(4) = 4^2 = 16 f(5) = 5^2 = 25 f(6) = 6^2 = 36Calculate Rectangle Areas: Multiply each function value by the width of the subintervals to find the area of each rectangle. Since the width of each subinterval is 1, the area of each rectangle is simply the function value at the right endpoint. Area of rectangle 1: 1 * f(3) = 1 * 9 = 9 Area of rectangle 2: 1 * f(4) = 1 * 16 = 16 Area of rectangle 3: 1 * f(5) = 1 * 25 = 25 Area of rectangle 4: 1 * f(6) = 1 * 36 = 36Sum Areas for Riemann Sum: Sum the areas of the rectangles to find the right Riemann sum approximation. Right Riemann sum = 9 + 16 + 25 + 36 = 86

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 right Riemann sum approximation for $\int_{2}^{6} x^{2} d x$ ? $\newline$ 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 right Riemann sum approximation for $\int_{2}^{6} x^{2} d x$ ? $\newline$ Round to the nearest thousandth if necessary. $\newline$ Answer: