Let f be the function defined by f(x)=5^(x). If six subintervals of equal length are used, what is the value of the right Riemann sum approximation for int_(0)^(1.5)5^(x)dx ? Round to the nearest thousandth if necessary. Answer:

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Let  f be the function defined by  f(x)=5^(x). If six subintervals of equal length are used, what is the value of the right Riemann sum approximation for  int_(0)^(1.5)5^(x)dx ? Round to the nearest thousandth if necessary. Answer:

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Divide into Subintervals: To approximate the integral using a right Riemann sum, we first need to divide the interval [0, 1.5] into six equal subintervals. This means each subinterval will have a length of (1.5 - 0) / 6.Calculate Subinterval Length: Calculate the length of each subinterval: (1.5 - 0) / 6 = 0.25.Identify Endpoints: Identify the endpoints of each subinterval. Since we are using a right Riemann sum, we will use the right endpoint of each subinterval to evaluate the function. The endpoints are: 0.25, 0.5, 0.75, 1.0, 1.25, and 1.5.Evaluate Function at Endpoints: Evaluate the function f(x) = 5^x at each of the right endpoints of the subintervals: f(0.25), f(0.5), f(0.75), f(1.0), f(1.25), f(1.5).Calculate Function Values: Calculate the value of the function at each endpoint: f(0.25) = 5^(0.25), f(0.5) = 5^(0.5), f(0.75) = 5^(0.75), f(1.0) = 5^(1.0), f(1.25) = 5^(1.25), f(1.5) = 5^(1.5).Calculate Rectangle Areas: Multiply each function value by the length of the subintervals (0.25) to get the area of each rectangle in the Riemann sum: Area1 = 0.25 * 5^(0.25), Area2 = 0.25 * 5^(0.5), Area3 = 0.25 * 5^(0.75), Area4 = 0.25 * 5^(1.0), Area5 = 0.25 * 5^(1.25), Area6 = 0.25 * 5^(1.5).Add Rectangle Areas: Add up the areas of all rectangles to get the right Riemann sum approximation: Right Riemann Sum = Area1 + Area2 + Area3 + Area4 + Area5 + Area6.Perform Calculations: Perform the calculations to find the sum: Right Riemann Sum = 0.25 * 5^(0.25) + 0.25 * 5^(0.5) + 0.25 * 5^(0.75) + 0.25 * 5^(1.0) + 0.25 * 5^(1.25) + 0.25 * 5^(1.5).Use Calculator: Use a calculator to find the numerical values of each term and sum them up: Right Riemann Sum ≈ 0.25 * 2.378414 + 0.25 * 2.236068 + 0.25 * 3.343702 + 0.25 * 5 + 0.25 * 7.450580 + 0.25 * 11.180340.Calculate Numerical Values: Calculate the sum: Right Riemann Sum ≈ 0.25 * 2.378414 + 0.25 * 2.236068 + 0.25 * 3.343702 + 0.25 * 5 + 0.25 * 7.450580 + 0.25 * 11.180340 ≈ 0.5946035 + 0.559017 + 0.8359255 + 1.25 + 1.862645 + 2.795085 ≈ 7.897276.Calculate Sum: Round the result to the nearest thousandth: Right Riemann Sum ≈ 7.897.

Let $f$ be the function defined by $f(x)=5^{x}$ . If six subintervals of equal length are used, what is the value of the right Riemann sum approximation for $\int_{0}^{1.5} 5^{x} d x$ ? Round to the nearest thousandth if necessary. $\newline$ Answer:

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Let $f$ be the function defined by $f(x)=5^{x}$ . If six subintervals of equal length are used, what is the value of the right Riemann sum approximation for $\int_{0}^{1.5} 5^{x} d x$ ? Round to the nearest thousandth if necessary. $\newline$ Answer: