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integral


Guest Chris123

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Guest Chris123

Dear all

 

Before I say anything, I must congratulate you on this fantastic website...so there really ARE other people who almost 'enjoy' maths too!

 

My problem is as followed...

 

Determine all the values of the real number c for which the following integral converges:

 

(the integral from infinity to zero of) (x^c) / sqrt (x^4 + x) dx

 

My first step was to split the ingral into two components A and B...

 

A= (the integral from 1 to zero) (x^c) / sqrt (x^4 + x) dx

 

 

B= (the integral from infinity to 1) (x^c) / sqrt (x^4 + x) dx

 

 

Is this the logical thing to do? So that then you can work out which real values each integral is smaller or equal to and subsequently compare?

 

Thank you for listening,

 

Chris

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so your saying that the reciprocal of Zero isn`t exactly infinity but every/any number between zero and infinity?

 

wouldn`t that be the same thing though or is it some weird maths stuff? (I`m hoping to take pre-university entry

maths this year, so you can tell I`m certainly no expert). I am still non the less intrigued by this ;)

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It's all about definition.

 

Say 1/0 = x

 

By the axioms we define, this must mean that x * 0 = 1. No number can be defined so that this operation is correct, hence the operation 1/0 is undefined.

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as for the original question, i'm not really able to understand it tbh - if x = 0 initially you have a problem no matter what value of c you use. is this actually meant to be a find the integral question or draw lots of graphs out, or what?

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