Calculus Calculus Math Forum

 March 30th, 2019, 12:36 PM #1 Senior Member   Joined: Dec 2015 From: Earth Posts: 820 Thanks: 113 Math Focus: Elementary Math Evaluate integral How to evaluate the integral ? $\displaystyle \int_{0}^{1} x^{n} e^x dx \; \;$ , $\displaystyle n\in \mathbb{N}$. March 30th, 2019, 03:17 PM #2 Global Moderator   Joined: May 2007 Posts: 6,852 Thanks: 743 Repeated integrate by parts. $\int_0^1x^ne^xdx=x^ne^x]_0^1-n\int_0^1x^{n-1}e^xdx$ The first term $=e$. Keep going till you hit 0. Thanks from topsquark and idontknow March 31st, 2019, 03:42 PM #3 Senior Member   Joined: Dec 2015 From: Earth Posts: 820 Thanks: 113 Math Focus: Elementary Math Got the answer like : $\displaystyle (-1)^{n-1}+e\sum_{j=0}^{n} (-1)^{n-j} \frac{n! }{j! }$. Tags evaluate, integral Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post WWRtelescoping Calculus 2 August 30th, 2014 03:18 PM zaidalyafey Calculus 6 August 26th, 2012 08:46 AM zaidalyafey Calculus 4 August 17th, 2012 11:23 AM lovetolearn Calculus 3 April 14th, 2012 04:47 PM ChloeG Calculus 1 March 1st, 2011 04:02 PM

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