Expression 5: "f" left parenthesis, "y" , right parenthesis equals left brace, "y" Subscript, 1 , Baseline left bracket, "n" , right bracket less than or equal to "y" less than or equal to "y" Subscript, 1 , Baseline left bracket, "n" plus 1 , right bracket : "S" times left parenthesis, "y" minus "y" Subscript, 1 , Baseline left bracket, "n" , right bracket , right parenthesis plus "x" Subscript, 1 , Baseline left bracket, "n" , right bracket , 0 , right bracefy=y1n≤y≤y1n+1:S·y−y1n+x1n,0
5
Expression 6: "g" left parenthesis, "y" , right parenthesis equals Start sum from "b" equals 1 to "f" left parenthesis, "y" , right parenthesis ., end sum, "f" left parenthesis, "y" , right parenthesis left bracket, "b" , right bracketgy=fy.length∑b=1fyb
6
Expression 7: "t" Subscript, 1 , Baseline equals pi Start integral from 0.0 4 to 1.8 6, end integral, "g" left parenthesis, "y" , right parenthesis squared "d" "y"t1=π∫1.860.04gy2dy
equals=
1.0 8 0 1 5 9 9 1 6 2 41.08015991624
7
Expression 8: "f" Subscript, 1 , Baseline equals pi Start integral from 0.0 4 to 0.9 7, end integral, "g" left parenthesis, "y" , right parenthesis squared "d" "y"f1=π∫0.970.04gy2dy