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

given the graph of the function f(x) below, use a left 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 left 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 width of rectangles

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

Step2: Identify left - hand endpoints

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

Step3: Read function values from graph

From the graph, $f(2)=9$, $f(3)=8$, $f(4)=6$, $f(5)=8$.

Step4: Calculate left Riemann sum

The left Riemann sum $L_4=\sum_{i = 1}^{4}f(x_i)\Delta x$. Substitute values: $L_4=f(2)\times1+f(3)\times1+f(4)\times1+f(5)\times1=(9 + 8+6 + 8)\times1=31$.

Answer:

$31$