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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 :((
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 :((

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You 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.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0We 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.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but that doesnt make sense, i just did the math, it converges only when p>1 ....
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