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

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Answer 1 · 2016-08-01T13:48:01

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

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 $0$ .

$=1-0$

$=1$

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