Question

3.3 Evaluate the Riemann sum for 𝑓(𝑥) = 2 + 6𝑥, 2 ≤ 𝑥 ≤ 14, with six sub intervals taking the sample point to be left end points. Hence evaluate the following integral
14
∫ (2 + 6𝑥) 𝑑𝑥.
2

Answer 1

with 6 subintervals, the left endpoints are 3,4,6,8,10,12
The interval width is 2, so just add up
2(f(2)+f(4)+...+f(12))