Help with convergent/divergent integrals?

Question

I'm working on a very difficult Calc. II project involving divergent and convergent integrals. I was wondering if anyone knew of a website that listed divergent or convergent integrals. Or, if you could help me out with this problem:

the integral of F(x) from 1 to infinity is divergent, the integral of G(x) from 1 to infinity is divergent, and the integral of F(x) - G(x) from 1 to infinity is convergent. I have to find two functions that will fit into this problem. I have tired numberous things and have come up with nothing. Thanks everyone.

Answer 1

F(x) = x + 1 and G(x) = x is a bad example because the integral of 1 is divergent.

But it was a good idea because you can always take F(x) = G(x) + H(x) with the integral of H(x) being convergent.

For example :

F(x) = e^x + 1/x² and G(x) = e^x

You have too :

F(x) = ch(x) = (e^x + e^(-x))/2 and
G(x) = sh(x) = (e^x - e^(-x))/2

F(x) - G(x) = e^(-x) and its integral is convergent

Answer 2

I am a little rusty on this, but couldn't you just have
F(x) = x+1, and G(x) = x ?

Answer 3

Do your own homework, kid.