Calculating upper and lower limits for a linear function

Question

I am asked to calculate the lower limit and upper limit (L₅ and U₅) for the linear function y=13-3x, between x=0 and x=4.

 

I have found that Δx=4/5, and that x₀ =0. However, I am getting my answers wrong when calculating x_1, x₂, ... x₅.

 

For example, I tried to calculate x₁ by doing n/2 = 1/2, however this is incorrect.

 

Any help would be greatly appreciated. Thank you!

Answer 1

What I think you are asking is the value of the upper and lower sum for the partition which has 4 equal intervals between 0 and 5.  Please note that there will be 5 points of the partition: x = 0, 1, 2, 3, 4 where y = 13, 10, 7, 4, 1 Δx = 1 (not 4/5).

 

Therefore, your lower sum will be 22 (10 + 7 + 4 + 1) and your upper sum will be 34 (13 + 10 + 7 + 4).

 

If this doesn't help, please let me know.