(NOTE: I am using an example in my book, that I have the answer to already, because I want to understand how they arrived at the answer, that way, I can do the other problems on my own)
Okay, so here is the problem:
Approximate the area under the curve on the given interval using n rectangles and the evaluation rules (a) left endpoint, (b) midpoint, and (c) right endpoint.
y = x2 + 1 on [0, 1] and n=16
So, this is how the book solved this.....
(a) ci = i∆x where i is from 0 to 15
A16 = ∆x (I do not know how to input the correct symbol here, but its 15 on top and i=0 on bottom) f(ci)
= 1/16 (that symbol again) [(i/16 + 1/16)2+ 1]
(approximately =) 1.3652
Now, I sort of get how they get up to the last part, but I do not understand how they came to the conclusion of 1.3652. Any clarification on this would be greatly appreciated.