selected values of $f(x)$ are shown in the table below. what is the trapezoidal sum approximation for…

selected values of $f(x)$ are shown in the table below. what is the trapezoidal sum approximation for $int_{3}^{14}f(x)dx$ using 5 subintervals as indicated by the table?\n3 6 8 11 13 14\n6 21 27 36 34 31\nanswer\nattempt 1 out of 2\nsubmit answer

selected values of $f(x)$ are shown in the table below. what is the trapezoidal sum approximation for $int_{3}^{14}f(x)dx$ using 5 subintervals as indicated by the table?\n3 6 8 11 13 14\n6 21 27 36 34 31\nanswer\nattempt 1 out of 2\nsubmit answer

Answer

Explanation:

Step1: Determine the width of sub - intervals

The interval is from $a = 3$ to $b = 14$ and $n=5$. The width of each sub - interval $\Delta x=\frac{b - a}{n}=\frac{14 - 3}{5}=\frac{11}{5}=2.2$.

Step2: Write the trapezoidal rule formula

The trapezoidal rule for $n$ sub - intervals is $T_n=\frac{\Delta x}{2}[f(x_0)+2f(x_1)+2f(x_2)+\cdots+2f(x_{n - 1})+f(x_n)]$. Here, $x_0 = 3,f(x_0)=6$; $x_1 = 6,f(x_1)=21$; $x_2 = 8,f(x_2)=27$; $x_3 = 11,f(x_3)=36$; $x_4 = 13,f(x_4)=34$; $x_5 = 14,f(x_5)=31$.

Step3: Calculate the trapezoidal sum

$T_5=\frac{2.2}{2}[6 + 2\times21+2\times27+2\times36+2\times34+31]$ $=1.1[6 + 42+54+72+68+31]$ $=1.1\times273$ $=300.3$

Answer:

$300.3$