overall accuracy: 87.2% record: 35 score: 35 selected values from the function f(x) are shown in the table…
overall accuracy: 87.2% record: 35 score: 35 selected values from the function f(x) are shown in the table below. when a right riemann sum with two subintervals is used to approximate ∫₂⁵ f(x)dx, the value is x 2 4 5 f(x) 2 5 2 12 9 15 10 high score board: overall refresh you must have at least 100 to be on the board. # name record
Answer
Explanation:
Step1: Determine sub - interval widths
The interval is from $a = 2$ to $b = 5$. With $n=2$ subintervals, $\Delta x=\frac{b - a}{n}=\frac{5 - 2}{2}=1.5$.
Step2: Identify right - hand endpoints
The subintervals are $[2,3.5]$ and $[3.5,5]$. The right - hand endpoints are $x_1 = 4$ and $x_2 = 5$.
Step3: Calculate right Riemann sum
The right Riemann sum $R_2=\sum_{i = 1}^{2}f(x_i)\Delta x=f(4)\times1.5+f(5)\times1.5$. From the table, $f(4) = 5$ and $f(5)=2$. So $R_2=(5\times1.5)+(2\times1.5)=7.5 + 3=10.5\approx10$ (rounding to the nearest integer among the options).
Answer:
10