Question

Problem 23. (1 point) Consider the integral (a) Find the Riemann sum for this integral using right endpoints and n = 4 (b) Find the Riemann sum for this same integral, using left endpoints and n= 4

Answer 1

n = 4 , so, divide the interval to 4 sections

and find the value of f(x) at the midpoint of each interval

So, from 2 to 6

x = 2 , 3 , 4 , 5 , 6

At x = 2.5

w = 1 , h = 3/2.5 + 1 = 2.2

wh = 2.2

at x = 3.5

w = 1 , h = 3/3.5 + 1 = 13/7

wh = 13/7

at x = 4.5

w = 1 , h = 3/4.5 + 1 = 5/3

wh = 5/3

at x = 5.5

w = 1 , h = 3/5.5 + 1 = 17/11

wh = 17/11

so, the sum of Riemann = 2.2 + 13/7 + 5/3 + 17/11 = 7.27