overall accuracy: 72.7% record: 6 score: 5 selected values from the function f(x) are shown in the table…
overall accuracy: 72.7% record: 6 score: 5 selected values from the function f(x) are shown in the table below. when a midpoint riemann sum with two subintervals is used to approximate ∫₂⁶ f(x)dx, the value is x 2 3 4 5 6 f(x) 1 2 4 1 3 6 9 8 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 width
The interval is from $a = 2$ to $b = 6$ and $n=2$. The width $\Delta x=\frac{b - a}{n}=\frac{6 - 2}{2}=2$.
Step2: Identify mid - points
The sub - intervals are $[2,4]$ and $[4,6]$. The mid - points are $x_1 = 3$ and $x_2 = 5$.
Step3: Calculate mid - point Riemann sum
The mid - point Riemann sum $M_2=\sum_{i = 1}^{2}f(x_i)\Delta x$. Here, $f(3)=2$, $f(5)=1$, and $\Delta x = 2$. So $M_2=(f(3)+f(5))\Delta x=(2 + 1)\times2=6$.
Answer:
6