Expression 10: "f" left parenthesis, 0 , right parenthesis plus Start sum from "i" equals 1 to "n" , end sum, left parenthesis, "f" left parenthesis, StartFraction, "i" Over "n" , EndFraction , right parenthesis minus "f" left parenthesis, StartFraction, "i" minus 1 Over "n" , EndFraction , right parenthesis , right parenthesis "s" left parenthesis, "w" times left parenthesis, "x" minus StartFraction, "i" minus 1 half Over "n" , EndFraction , right parenthesis , right parenthesisf0+n∑i=1fin−fi−1nsw·x−i−12n
10
The functions added together (along with f(0)) to make the approximation:
11
Expression 12: "i" Subscript, "a" "l" "l" , Baseline equals left bracket, 1 , ... , "n" , right bracketiall=1,...,n
equals=
11
22
33
44
55
66
77
88
99
1010
12
Expression 13: left parenthesis, "f" left parenthesis, StartFraction, "i" Subscript, "a" "l" "l" , Baseline Over "n" , EndFraction , right parenthesis minus "f" left parenthesis, StartFraction, "i" Subscript, "a" "l" "l" , Baseline minus 1 Over "n" , EndFraction , right parenthesis , right parenthesis "s" left parenthesis, "w" times left parenthesis, "x" minus StartFraction, "i" Subscript, "a" "l" "l" , Baseline Over "n" , EndFraction , right parenthesis , right parenthesisfialln−fiall−1nsw·x−ialln