My Math Forum Check if integral converges

 Real Analysis Real Analysis Math Forum

 October 29th, 2016, 10:05 AM #1 Newbie   Joined: Oct 2016 From: italy Posts: 9 Thanks: 0 Check if integral converges Hi guys, I've to verify if $\displaystyle \int_{1}^{+\infty} \frac{e^{-x}}{\sqrt x}dx$ converges. I use the convergence criteria: $\displaystyle \frac{e^{-x}}{\sqrt x} \leq \frac{1}{\sqrt x}$. The exponent of $\displaystyle x$ is $\displaystyle 1/2$ , for the convergence criteria this integral should not converge, but standing to wolfram (and to the book) it does. What am I doing wrong?
 October 29th, 2016, 10:15 AM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 6,344 Thanks: 2083 Math Focus: Mainly analysis and algebra The fact that your integrand is less than a divergent integrand tells you nothing. You need to find a divergent integrand that is less than yours to prove divergence or a convergent integrand greater than yours to prove convergence. ($e^{-x}$). Thanks from nostradamus1915
 October 29th, 2016, 11:37 AM #3 Newbie   Joined: Oct 2016 From: italy Posts: 9 Thanks: 0 So what should I do in this case?
 October 29th, 2016, 11:40 AM #4 Math Team   Joined: Dec 2013 From: Colombia Posts: 6,344 Thanks: 2083 Math Focus: Mainly analysis and algebra Try some functions. If your first attempt has failed, try to find another. Thanks from nostradamus1915 Last edited by v8archie; October 29th, 2016 at 12:06 PM.
 October 29th, 2016, 11:59 AM #5 Newbie   Joined: Oct 2016 From: italy Posts: 9 Thanks: 0 Wait, a convergent integrand greater than this is $\displaystyle e^{-x}$ ! p.s.: Oh you wrote that, didn't notice xD
 October 29th, 2016, 12:06 PM #6 Math Team   Joined: Dec 2013 From: Colombia Posts: 6,344 Thanks: 2083 Math Focus: Mainly analysis and algebra Well done. Thanks from nostradamus1915

 Tags check, converges, integral

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post tuphaan Calculus 2 March 22nd, 2016 06:20 PM OriaG Calculus 3 February 27th, 2013 11:24 AM patient0 Calculus 4 May 30th, 2011 11:13 AM cxc001 Calculus 3 September 9th, 2010 06:54 AM nedaiii Real Analysis 1 February 8th, 2009 08:15 PM

 Contact - Home - Forums - Top