Let f be the function defined by f(x)=3^(x). If three subintervals of equal length are used, what is the value of the trapezoidal sum approximation for int_(0)^(3)3^(x)dx ? Round to the nearest thousandth if necessary. Answer:

Question

Let  f be the function defined by  f(x)=3^(x). If three subintervals of equal length are used, what is the value of the trapezoidal sum approximation for  int_(0)^(3)3^(x)dx ? Round to the nearest thousandth if necessary. Answer:

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Understand trapezoidal rule: Understand the trapezoidal rule and set up the problem. The trapezoidal rule is a numerical method to approximate the definite integral of a function. It works by dividing the interval of integration into smaller subintervals, then approximating the area under the curve for each subinterval by the area of a trapezoid. The formula for the trapezoidal rule with n subintervals is: T = (Δx/2) * (f(x_0) + 2f(x_1) + 2f(x_2) + ... + 2f(x_{n-1}) + f(x_n)) where Δx is the width of each subinterval, and x_0, x_1, ..., x_n are the endpoints of the subintervals. In this case, we are using three subintervals to approximate the integral from 0 to 3, so Δx = (3 - 0)/3 = 1.Calculate function values: Calculate the function values at the endpoints of the subintervals. We need to evaluate the function f(x) = 3^x at the endpoints of the subintervals, which are x = 0, x = 1, x = 2, and x = 3. f(0) = 3^0 = 1 f(1) = 3^1 = 3 f(2) = 3^2 = 9 f(3) = 3^3 = 27Apply trapezoidal rule: Apply the trapezoidal rule to approximate the integral. Using the trapezoidal rule formula: T = (Δx/2) * (f(0) + 2f(1) + 2f(2) + f(3)) T = (1/2) * (1 + 2*3 + 2*9 + 27) T = (1/2) * (1 + 6 + 18 + 27) T = (1/2) * 52 T = 26Round result: Round the result to the nearest thousandth if necessary. Since the result is an integer, there is no need to round it. The value of the trapezoidal sum approximation is 26.

Let $f$ be the function defined by $f(x)=3^{x}$ . If three subintervals of equal length are used, what is the value of the trapezoidal sum approximation for $\int_{0}^{3} 3^{x} d x$ ? Round to the nearest thousandth if necessary. $\newline$ Answer:

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Let $f$ be the function defined by $f(x)=3^{x}$ . If three subintervals of equal length are used, what is the value of the trapezoidal sum approximation for $\int_{0}^{3} 3^{x} d x$ ? Round to the nearest thousandth if necessary. $\newline$ Answer: