integral

[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

[YT2095]

forgive me if I`m way off base here, but isn`t Zero just the reciprocal of infinty and vice versa anyways?

[Dave]

Not quite. 1/0 ≠ infinity, there are just an infinite number of numbers which the answer could be.

[YT2095]

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

[Dave]

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.

[YT2095]

a bit like the "Division by Zero Error" my computer takes great delight in telling me for no reason when I`m in the middle of something interesting

[Dave]

yeah, thats it.

[Dave]

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?