selected values from the function f(x) are shown in the table below. when a trapezoidal sum with two…
selected values from the function f(x) are shown in the table below. when a trapezoidal sum with two subintervals is used to approximate ∫₁⁴ f(x)dx, the value is x 1 3 4 f(x) 5 1 5 3 7 11 9
Answer
Answer:
7
Explanation:
Step1: Recall trapezoidal - sum formula
$T_n=\frac{\Delta x}{2}[f(x_0)+2f(x_1)+\cdots + 2f(x_{n - 1})+f(x_n)]$, where $\Delta x=\frac{b - a}{n}$. Here, $a = 1$, $b = 4$, $n = 2$, so $\Delta x=\frac{4 - 1}{2}=\frac{3}{2}$.
Step2: Identify function - values
$x_0 = 1$, $f(x_0)=5$; $x_1 = 3$, $f(x_1)=1$; $x_2 = 4$, $f(x_2)=5$.
Step3: Apply trapezoidal - sum formula
$T_2=\frac{\Delta x}{2}[f(x_0)+2f(x_1)+f(x_2)]=\frac{3/2}{2}[5 + 2\times1+5]=\frac{3}{4}(5 + 2+5)=\frac{3}{4}\times12 = 7$.