Expression 6: "g" left parenthesis, "x" , right parenthesis equals left parenthesis, StartFraction, beta minus alpha Over "b" minus "a" , EndFraction , right parenthesis left parenthesis, "x" minus "a" , right parenthesis plus alphagx=β−αb−ax−a+α
6
Expression 7: "n" left parenthesis, "x" , right parenthesis equals "e" Subscript, "p" "s" "i" "l" "o" "n" , Baseline left parenthesis, "a" minus "x" , right parenthesis left parenthesis, "b" minus "x" , right parenthesisnx=epsilona−xb−x
7
Expression 8: "f" left parenthesis, "x" , right parenthesis equals "g" left parenthesis, "x" , right parenthesis plus "n" left parenthesis, "x" , right parenthesis left brace, "a" less than "x" less than "b" , "b" less than "x" less than "a" , right bracefx=gx+nxa<x<b,b<x<a
8
A: left parenthesis, "a" , alpha , right parenthesisa,α
Label:
equals=
left parenthesis, 4.3 6 , 1.9 8 , right parenthesis4.36,1.98
9
B: left parenthesis, "b" , beta , right parenthesisb,β
Label:
equals=
left parenthesis, 7.5 8 , 0.3 5 , right parenthesis7.58,0.35
10
Expression 11: "s" equals Start integral from 0 to 1, end integral, StartRoot, 1 plus left parenthesis, StartFraction, beta minus alpha Over "b" minus "a" , EndFraction plus "n" prime left parenthesis, "x" , right parenthesis , right parenthesis squared , EndRoot "d" "x"s=∫101+β−αb−a+n′x2dx
equals=
7.2 2 1 5 8 1 0 4 7 47.2215810474
11
Arc Length=${s} left parenthesis, StartFraction, left parenthesis, "a" plus "b" , right parenthesis minus 1 Over 2 , EndFraction , StartFraction, left parenthesis, alpha plus beta , right parenthesis Over 2 , EndFraction , right parenthesisa+b−12,α+β2
Label:
equals=
left parenthesis, 5.4 7 , 1.1 6 5 , right parenthesis5.47,1.165