It is given that f(x) = a + b -
x
=
x)dx
=
dx
= a(b^2 - a^2)/2 + b(b^2 - a^2)/2 - (b^3 -
a^3)/3
= ab^2/2 - a^3/2 + b^3/2 - ba^2/2 - b^3/3 + a^3/3
...(1)
[(a + b)/2] = [(a + b)/2]*
+ b - x)dx
= [(a + b)/2]*[a(b - a) + b(b - a) - (b^2 -
a^2)/2]
= a(b^2 - a^2)/2 + b(b^2 - a^2)/2 - (b^3 + a*b^2
- a^2*b - a^3)/4
= ab^2/2 - a^3/2 + b^3/2 - ba^2/2 - b^3/4
- ab^2/4 - a^2*b/4 - a^3/4 ...(2)
(1) and (2) are not
equal.
It is not true that = [(a +
b)/2]*
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