Converge and Diverge

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Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not, state your answer as divergent  

integral from three to infinity of ln(x)/x

Apr 8th, 2015

it is divergent....................................................................................................

Apr 8th, 2015

why?

Apr 8th, 2015

when we  evaluate the limit it becomes infinity......

so this is divergent.....................

Apr 8th, 2015

Very sorry my friend, I am terrible in math, so I was wondering if you could posting how you got there? (steps)

Apr 8th, 2015

ok...

Apr 8th, 2015

∫ [ ln(x) / x ] dx for x = 3 to x = + infinity 

Use substitution u = ln(x), then du = (1/x) dx, and the integral is 

∫ u du = [ u^2 / 2 ] + C

           = [ ln^2(x) /2 ] + C.

             To check for  converges, you have to do the indefinite integral from x = 3 to x = + infinity 

limit -> + infinity [ ln^2(x) / 2 ] when x at t = + infinity and t = 3

          = + infinity.

so it is divergent.......................................................

Apr 8th, 2015

hope you understood........thank you

Apr 8th, 2015

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