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.