Question

find out for what value of p the improper integral
+∞
∫ 1/x^p dx converge.
1


tough questions,,,, i need an explaintion :((

Answer 1

0?

Answer 2

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.

Answer 3

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.

Answer 4

THANKS ALOT

Answer 5

Become a fan :)

Answer 6

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