evaluate the integral `int_1^oo (lnx/x) dx`

Calculus 1 and 2 questions with single variable are posted here.

Moderator: ChangBroot

Forum rules
To type int use \`int\` and the same way to type sqrt simply type \`sqrt\` or Please view the examples forum.

As you type, live preview is displayed so you know exactly what are you typing.

evaluate the integral `int_1^oo (lnx/x) dx`

Postby barnamah » Mon 20 June, 2011 12:47

evaluate the integral `int(lnx/x) dx` from x=1 to `x=oo`
Explore and know. That is asked.
User avatar
Posts: 102
Joined: Mon 14 March, 2011 08:37
Location: Canada

Re: evaluate the integral `int_1^oo (lnx/x) dx`

Postby Integr88 » Mon 20 June, 2011 12:49

this can be written as`int_1^oo (lnx/x) dx`
this is type 1 improper integral which the bounds are between 1 and `oo`
using limit we can solve this:

let u=lnx, du=`1/xdx`
`lim_(t->oo)int_1^tudu` and integrate `lim_(t->oo)[u^2/2]_1^t`
In previous step we set u=ln x so substitute it into our equation and we have `lim_(t->oo)[(lnx)^2/2]_1^t` evaluate with t and 1
`:.` it is `oo` and diverging.
User avatar
Posts: 71
Joined: Tue 15 March, 2011 13:27

Return to Calculus single variable

Who is online

Users browsing this forum: No registered users and 1 guest