My Math Forum Improper integral of a function

 Calculus Calculus Math Forum

November 21st, 2018, 08:06 AM   #1
Newbie

Joined: Oct 2015
From: algeria

Posts: 5
Thanks: 0

Improper integral of a function

I want to study the nature of an improper integral. I separate the integral from 0 to 1 and from 1 to ∞. The first integral is divergent (I proved that it is equivalent to Riemann integral, which is divergent in the neighborhood of 0). But I didn't find how I can prove the convergence or divergence of the second one. The integral can be found in attach file.
Thank you
Attached Images
 intégral-.jpg (50.2 KB, 14 views)

 November 21st, 2018, 09:54 AM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,531 Thanks: 1390 It certainly looks like the integral blows up at multiples of $\pi$, i.e. where $\sin^2(x)=0$
 November 21st, 2018, 01:41 PM #3 Global Moderator   Joined: May 2007 Posts: 6,807 Thanks: 716 It is not divergent at x=0, since $log(1+x)^2\approx x^2$ there. However as romsek points out it will blow up at multiples of $\pi$.

 Tags function, improper, integral

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post DavidSzalai Calculus 1 March 19th, 2017 10:30 AM Stelios Calculus 0 September 5th, 2015 10:42 PM unwisetome3 Calculus 2 April 8th, 2013 10:45 AM ZardoZ Complex Analysis 10 April 13th, 2011 03:32 AM neonsubbs Calculus 7 March 5th, 2009 12:33 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top