9.3 Calculations

 

Calculation Of Rn[1, 3]

 

Fig. 2.1

 

Finding Areas.


See Fig. 2.1. Use a regular partition of order
n of [1, 3] and the left endpoints. The length of each sub-interval is
(3 1)/
n = 2/n. The left endpoints are:

 

 

Return To Section 9.3

 

Calculation Of Rn[0, 3]

 

Refer to Fig. 2.1. Utilize a regular partition of order n of [0, 3] and the left endpoints. The length of each sub-interval is
(3 0)/
n = 3/n. The left endpoints are xi = 0 + i(3/n) = i(3/n) for i = 0, 1, 2, ..., n 1, so they are:

 

 

Return To Section 9.3

 

 

Fig. 3.4

 

Upper Riemann Sum.

 

See Fig. 3.4. Recall that the endpoints are:

 

 

Return To Section 9.3