overall accuracy: 87.2% record: 29 score: 29 selected values from the function f(x) are shown in the table…
overall accuracy: 87.2% record: 29 score: 29 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 ∫₁⁶ f(x)dx, the value is x 1 4 6 f(x) 3 4 1 17 20 15 14 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 $a = 1$ to $b = 6$. With $n=2$ subintervals, $\Delta x=\frac{b - a}{n}=\frac{6 - 1}{2}=2.5$.
Step2: Identify right - hand endpoints
The subintervals are $[1,4]$ and $[4,6]$. The right - hand endpoints are $x_1 = 4$ and $x_2=6$.
Step3: Calculate right Riemann sum
The right Riemann sum $R_2=\sum_{i = 1}^{2}f(x_i)\Delta x=f(4)\times2.5+f(6)\times2.5$. Given $f(4) = 4$ and $f(6)=1$, we have $R_2=(4\times2.5)+(1\times2.5)=10 + 2.5=12.5$ (There seems to be an error in the problem - setup as the correct formula for two sub - intervals with the given $x$ values should use $\Delta x_1=4 - 1=3$ and $\Delta x_2=6 - 4 = 2$. Using the correct $\Delta x$ values: $R=\sum_{i = 1}^{2}f(x_i)\Delta x_i=f(4)\times(4 - 1)+f(6)\times(6 - 4)=4\times3+1\times2=12 + 2=14$).
Answer:
14