Determine if the improper integral is divergent or not

[Fatima Hasan]

Homework Statement

Determine if the improper integral is divergent or convergent .

Homework Equations

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The Attempt at a Solution

When i solved the first term using online calculator , the answer was "The integral is divergent" . However , I got 0 .
Where is my mistake ?

 

[Orodruin]

You cannot generally do things like $\infty - \infty = 0$. Furthermore, what you have is not $\infty - \infty$ as $1/[2(0^2 - 1)] = -1/2$.

 

[Fatima Hasan]

You cannot generally do things like $\infty - \infty = 0$. Furthermore, what you have is not $\infty - \infty$ as $1/[2(0^2 - 1)] = -1/2$.

It should be $-1/[2(1^2-1)] +- 1/[2(0^2-1)]= -1/0 + 1/2 = -\infty+1/2$
So , it's divergent . Right ?