Find the value V of the Riemann sum ∑ 𝑓(𝑐𝑘 )∆𝑥𝑘 𝑛 𝑘=1 for the function 𝑓(𝑥) = 2 𝑥 using the partition 𝑃 = {1,3,6,8}, where 𝑐𝑘 are the right end points of the partition V.

Answer 1

You can see there are three intervals and three right end points.

This can be best solved by creating a table like the following and in the end summing up the terms of summation:

k | c_k | Δ x_k | f(c_k )*Δ x_k

1 | 3 | 6 | 2* 3 *2 = 12

2 | 6 | 3 | 2* 6 *3 =36

3 | 8 | 2 | 2* 8 *2 = 32

V=12 + 36 + 32 = 80. (Ans)