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 left Riemann sum approximation for int_(1)^(2)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 left Riemann sum approximation for  int_(1)^(2)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 = 1 to x = 2 and we are using four subintervals, the width (Δx) of each subinterval is (2 - 1) / 4 = 0.25.Identify Left Endpoints: Identify the x-values for the left endpoints of each subinterval. The left endpoints for the subintervals are x = 1, x = 1.25, x = 1.5, and x = 1.75.Evaluate Function Values: Evaluate the function f(x) = x^2 at each of the left endpoints. f(1) = 1^2 = 1 f(1.25) = 1.25^2 = 1.5625 f(1.5) = 1.5^2 = 2.25 f(1.75) = 1.75^2 = 3.0625Calculate Rectangle Areas: Multiply each function value by the width of the subintervals to find the area of each rectangle. Area1 = f(1) * Δx = 1 * 0.25 = 0.25 Area2 = f(1.25) * Δx = 1.5625 * 0.25 = 0.390625 Area3 = f(1.5) * Δx = 2.25 * 0.25 = 0.5625 Area4 = f(1.75) * Δx = 3.0625 * 0.25 = 0.765625Sum Rectangle Areas: Sum the areas of the rectangles to find the left Riemann sum approximation. Left Riemann Sum = Area1 + Area2 + Area3 + Area4 = 0.25 + 0.390625 + 0.5625 + 0.765625Calculate Total Sum: Calculate the total sum to find the approximation. Left Riemann Sum = 0.25 + 0.390625 + 0.5625 + 0.765625 = 1.96875

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 left Riemann sum approximation for $\int_{1}^{2} x^{2} d x$ ? 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 left Riemann sum approximation for $\int_{1}^{2} x^{2} d x$ ? Round to the nearest thousandth if necessary. $\newline$ Answer: