Question

given the following table of values for f(x):
x = 1 2 3 4 5 6 7
f(x) = 1 6 1 9 -6 3 -2
evaluate the riemann sum for f(x), 1 ≤ x ≤ 7 with three equal sub - intervals and taking the sample points to be the left endpoints.
riemann sum = □

Explanation:

Step1: Calculate subinterval width

$\Delta x = \frac{7-1}{3} = 2$

Step2: Identify left endpoints

Left endpoints: $x=1,3,5$ with $f(x)=1,1,-6$

Step3: Compute Riemann sum

Sum = $\Delta x[f(1)+f(3)+f(5)] = 2[1+1+(-6)]$

Step4: Simplify the expression

$2[1+1-6] = 2(-4) = -8$

Answer:

-8