Improper integral concept help.

[frasifrasi]

Ok, my book has the example int from -1 to 2 of dx/x^3

this gets split into int from -1 to 0 of dx/x^3 and int from 0 to 2 of dx/x^3.

Now, he had previously determined that the second integral returned positive infinity (diverges) by taking the lim as b approaches 0+.


So, the book goes on to say that since the second integral diverges the original integral also diverges.

--> but what does that mean? is "divergers" the answer to "evaluate the int from -1 to 2 of dx/x^3" ? Or does it mean the the answer is just infinity?

Can anyone explain?

 

[arildno]

It means that it diverges.

 

[frasifrasi]

so what is the answer ? what does this mean ?? what should I conclude from this? does it mean that I shoudl stope evaluating the original improper integral?

I would appreciate HELPFUL input. If you aren't going to clarify the solution, please igonre the thread.

 

[arildno]

so what is the answer ?

There is none.

what does this mean ?? what should I conclude from this?

That the expression is meaningless.

does it mean that I shoudl stope evaluating the original improper integral?

Quite so.