## anonymous 5 years ago find out for what value of p the improper integral +∞ ∫ 1/x^p dx converge. 1 tough questions,,,, i need an explaintion :((

1. anonymous

0?

2. anonymous

You need to consider specific cases for p. You set the problem up like this$\lim_{c \rightarrow \infty} \int\limits_{1}^{c}\frac{1}{x^p}dx$and consider when: 1. p=1 2. p<1 3. p>1 The integral will only converge for p<1, but I'll leave you to have a go at the mathematics. If you need anything else, let me know.

3. anonymous

We have to set the integral up as above since this is Riemannian integration, which is only defined on intervals not including +/- infinity. Once we integrate, that's when we can use limits to determine the value.

4. anonymous

THANKS ALOT

5. anonymous

Become a fan :)

6. anonymous

but that doesnt make sense, i just did the math, it converges only when p>1 ....