Question

How do you evaluate the integral `int 1/x^2 dx` from 1 to `oo`?

Answer 1

`int_1^oo 1/x^2dx=1`

Explanation:

We have:

`int_1^oo1/x^2dx=int_1^oox^-2dx=lim_(trarroo)int_1^tx^-2dx`

Using the typical integration rule:

`=lim_(trarroo)[-1/x]_1^t`

`=lim_(trarroo)(-1/t-(-1/1))`

`=lim_(trarroo)(1-1/t)`

Note that as `x` approaches `oo`, `1/t` goes to `0`.

`=1-0`

`=1`