question given the graph of the function f(x) below, use a right riemann sum with 4 rectangles to…

Explanation:

Step1: Calculate the width of each rectangle

The interval is from $a = 1$ to $b = 5$, and $n=4$. The width $\Delta x=\frac{b - a}{n}=\frac{5 - 1}{4}=1$.

Step2: Identify the right - hand endpoints

The right - hand endpoints of the 4 sub - intervals $[1,2]$, $[2,3]$, $[3,4]$, $[4,5]$ are $x_1 = 2$, $x_2=3$, $x_3 = 4$, $x_4=5$.

Step3: Find the function values at the right - hand endpoints

From the graph, $f(2)=7$, $f(3)=8$, $f(4)=5$, $f(5)=3$.

Step4: Calculate the right Riemann sum

$R_4=\sum_{i = 1}^{4}f(x_i)\Delta x=f(2)\Delta x+f(3)\Delta x+f(4)\Delta x+f(5)\Delta x$. Substitute $\Delta x = 1$ and the function values: $R_4=(7\times1)+(8\times1)+(5\times1)+(3\times1)=7 + 8+5 + 3=23$.

Answer:

23