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

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:

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: 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 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, $f(3)=4$, $f(4)=5$, $f(5)=9$, $f(6)=8$.

Step4: Calculate the right Riemann sum

The right Riemann sum $R_4=\sum_{i = 1}^{4}f(x_i)\Delta x$. Substitute the values: $R_4=f(3)\times1 + f(4)\times1+f(5)\times1 + f(6)\times1=(4 + 5+9 + 8)\times1=26$.

Answer:

26