given the graph of the function f(x) below, use a right riemann sum with 3 rectangles to approximate the…

given the graph of the function f(x) below, use a right riemann sum with 3 rectangles to approximate the integral ∫₂⁵ 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 3 rectangles to approximate the integral ∫₂⁵ f(x) dx. give your answer rounded to the nearest tenth, if necessary. provide your answer below:

Answer

Explanation:

Step1: Calculate width of rectangles

The interval is from $a = 2$ to $b = 5$ and $n=3$. The width $\Delta x=\frac{b - a}{n}=\frac{5 - 2}{3}=1$.

Step2: Identify right - hand endpoints

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

Step3: Find function values at endpoints

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

Step4: Calculate right Riemann sum

The right Riemann sum $R_3=\sum_{i = 1}^{3}f(x_i)\Delta x=f(3)\times1+f(4)\times1+f(5)\times1=7\times1 + 5\times1+4\times1=7 + 5+4=16$.

Answer:

$16$