Assume that f and g are continuous on [a,b] and
Does it necessarily follow that for all ?
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Take for instance f(x) = 1/2 and g(x) = x over [-1,1]
No, put and for
But (At least not always.)
(Anyway, the converse is true.)
The converse is not true however.
Similar to the graph given by running-gag,
when integrated, gives 2.
when integrated over the same interval gives
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