Find values for which this integral diverges

I have the following question, I have to find the values of a for which the indefinite integral of x^{-a} from 1 to infinity diverge.

Substitution h for infinity I get: limit h->0 (1/(a-1)-h1^{-y}/(a-1))

So it diverges only for a=1 because there the limit is not defined! Is this correct?

Re: Find values for which this integral diverges

If then, . If , then and the integral is divergent. If then, . Easily proved:

Re: Find values for which this integral diverges

Thank you! I didn't thought about writing x^{-a} as 1/x^{a}

Re: Find values for which this integral diverges

Quote:

Originally Posted by

**FernandoRevilla** If

then,

.

Of course I meant instead of .

Re: Find values for which this integral diverges

If I do the same exercise with the Integral from 0 to infinity, it diverges for every "a" - is this true?

Re: Find values for which this integral diverges

What a satisfaction, I found the solution... I was wrong.

It converges for a<1 and diverges for a >1

Re: Find values for which this integral diverges

Quote:

Originally Posted by

**FernandoRevilla** If

then,

. If

, then

and the integral is divergent. If

then,

. Easily proved:

Of course the lower limit is instead of .

Re: Find values for which this integral diverges

Quote:

Originally Posted by

**FernandoRevilla** Of course I meant

instead of

.

Of course (again) the lower limit is instead of .