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

Explanation:

Step1: Calculate the width of each rectangle

The interval is from $a = 2$ to $b=6$, and $n = 4$. The width $\Delta x=\frac{b - a}{n}=\frac{6 - 2}{4}=1$.

Step2: Determine the right - hand endpoints

The right - hand endpoints of the 4 sub - intervals $[2,3]$, $[3,4]$, $[4,5]$, $[5,6]$ are $x_1 = 3$, $x_2 = 4$, $x_3 = 5$, $x_4 = 6$.

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

From the graph, $f(3)=5$, $f(4)=4$, $f(5)=6$, $f(6)=9$.

Step4: Calculate the right Riemann sum

The right Riemann sum $R_4=\sum_{i = 1}^{4}f(x_i)\Delta x$. Substitute the values: $R_4=f(3)\times1+f(4)\times1+f(5)\times1+f(6)\times1=(5 + 4+6 + 9)\times1=24$.

Answer:

24