1.

Proceedingfrom geometric reasoning, prove that : (a)if the function f(x)increases and has a concave graph in theinterval [a,b], then (b,a) f (a) lt int_(a)^(b) f(x) dx lt (b-a)""(f(a) + f(b))/(2) (b) if thefunction f(x) increases andhas a convexgraph in theinterval [a,b], then (b-a) ""(f(a) + f(b))/(2) lt int_(a)^(b) f(x) dx lt (b - a) f(b)

Answer»


Answer :Theinequality
`(B-a) f(a) LT int_(a)^(b) f(x) DX ` is OBVIOUS.


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