overall accuracy: 81.3% record: 10 score: 10 selected values from the function f(x) are shown in the table…
overall accuracy: 81.3% record: 10 score: 10 selected values from the function f(x) are shown in the table below. when a trapezoidal sum with two subintervals is used to approximate ∫₂⁷ f(x)dx, the value is x 2 5 7 f(x) 3 5 3 19 25 21 20 high score board: overall refresh you must have at least 100 to be on the board. # name record
Answer
Explanation:
Step1: Recall trapezoidal - sum formula
The trapezoidal - sum formula for $n$ sub - intervals on $[a,b]$ is $T_n=\frac{\Delta x}{2}[f(x_0)+2f(x_1)+2f(x_2)+\cdots + 2f(x_{n - 1})+f(x_n)]$, where $\Delta x=\frac{b - a}{n}$. Here, $a = 2$, $b = 7$, and $n = 2$. So, $\Delta x=\frac{7 - 2}{2}=\frac{5}{2}$.
Step2: Identify function values
We have $x_0 = 2$, $f(x_0)=3$; $x_1 = 5$, $f(x_1)=5$; $x_2 = 7$, $f(x_2)=3$.
Step3: Apply the formula
$T_2=\frac{\Delta x}{2}[f(x_0)+2f(x_1)+f(x_2)]=\frac{5/2}{2}[3 + 2\times5+3]=\frac{5}{4}(3 + 10+3)=\frac{5}{4}\times16 = 20$.
Answer:
20