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

Explanation:

Step1: Calculate width of rectangles

The interval is from $a = 3$ to $b = 5$ and $n=4$. The width $\Delta x=\frac{b - a}{n}=\frac{5 - 3}{4}=0.5$.

Step2: Determine left - hand endpoints

The left - hand endpoints of the 4 sub - intervals are $x_1 = 3$, $x_2=3 + 0.5=3.5$, $x_3=3.5 + 0.5 = 4$, $x_4=4 + 0.5=4.5$.

Step3: Find function values at endpoints

From the graph, $f(3)=6$, $f(3.5)=4$, $f(4)=2$, $f(4.5)=1$.

Step4: Calculate left Riemann sum

The left Riemann sum $L_4=\sum_{i = 1}^{4}f(x_i)\Delta x=\Delta x(f(3)+f(3.5)+f(4)+f(4.5))=0.5(6 + 4+2 + 1)=0.5\times13 = 6.5$.

Answer:

6.5