General feature of Newton Integral

dapet

Hi,

I need a help with responding one question from my calculus classes...

Lef f: [0, + infin.) ---> R be a continuous function and let exist the finite Newton integral of f(x) dx from 0 to +infinity. It´s neccesary that f is bounded?

Thanks for any help.

HallsofIvy

I'm not sure what you mean by "the finite Newton integral". Do you mean to assert that the Riemann integral is finite?

dapet

By Newton Integral I mean the integral of f(x) dx from a to b defined as follows, let F be a primtive function to f then the discussed integral is equal to F(b) - F(a) or [lim (x --> b-) F(x) - lim (x --> a+) F(x)] and the Riemanns definition of integral is based on the areas in the graph. So the task demands to proof it only from the Newton's definition.