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

question given the graph of the function f(x) below, use a right riemann sum with 4 rectangles to approximate the integral ∫₂⁶ f(x) dx. give your answer rounded to the nearest tenth, if necessary. provide your answer below:

question given the graph of the function f(x) below, use a right riemann sum with 4 rectangles to approximate the integral ∫₂⁶ f(x) dx. give your answer rounded to the nearest tenth, if necessary. provide your answer below:

Answer

Explanation:

Step1: Determine 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: Identify 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: Find the function values at the right - hand endpoints

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

Step4: Calculate the right Riemann sum

The right Riemann sum $R_4=\sum_{i = 1}^{4}f(x_i)\Delta x=f(3)\times1+f(4)\times1+f(5)\times1+f(6)\times1$. Substitute the values: $R_4=4\times1 + 3\times1+6\times1+9\times1=4 + 3+6+9=22$.

Answer:

$22$