Calculus Calculus Math Forum

February 16th, 2015, 09:07 AM   #1
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Checking mistake

Where did I make mistake ?
My answer is $\displaystyle \frac{1}{4}\pi^2+2$. The correct answer is $\displaystyle \frac{1}{4}\pi^2-2$.
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Last edited by jiasyuen; February 16th, 2015 at 09:14 AM. February 16th, 2015, 09:19 AM #2 Senior Member   Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 522 Math Focus: Calculus/ODEs The second time you applied integration by parts, you did not distribute the negative sign to the resulting integral.  February 16th, 2015, 09:31 AM #3 Math Team   Joined: Jul 2011 From: Texas Posts: 3,101 Thanks: 1677 obviously a sign error ... $\displaystyle \int x^2\cos{x} \, dx$ $\displaystyle u = x^2$ ; $\displaystyle du = 2x \, dx$ $\displaystyle dv = \cos{x} \, dx$ ; $\displaystyle v = \sin{x}$ $\displaystyle \int x^2\cos{x} \, dx = x^2\sin{x} - \int 2x\sin{x} \, dx$ $\displaystyle u = 2x$ ; $\displaystyle du = 2 \, dx$ $\displaystyle dv = \sin{x}$ ; $\displaystyle v = -\cos{x} \, dx$ $\displaystyle \int x^2\cos{x} \, dx = x^2\sin{x} - \left[-2x\cos{x} - \int -2\cos{x} \, dx\right]$ ... from this step to the next is where I think you made a sign error $\displaystyle \int x^2\cos{x} \, dx = x^2\sin{x} + 2x\cos{x} - \int 2\cos{x} \, dx$ Thanks from MarkFL February 16th, 2015, 03:07 PM #4 Senior Member   Joined: Sep 2013 From: Earth Posts: 827 Thanks: 36 Thanks a lot guys. I wonder when will the time I be one of you guys. February 16th, 2015, 04:03 PM   #5
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Math Focus: Calculus/ODEs
Quote:
 Originally Posted by jiasyuen Thanks a lot guys. I wonder when will the time I be one of you guys.
You are like me...that's exactly the kind of mistake I could make, and then just not see it.  February 16th, 2015, 06:56 PM #6 Global Moderator   Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms As Jesus once said, let he who has not made a sign error throw the first stone. Something like that, anyway. Tags checking, mistake 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 SXmath Calculus 1 February 9th, 2015 05:52 AM jiasyuen Calculus 3 January 30th, 2015 06:16 PM livestrong136 Calculus 1 May 8th, 2012 05:02 AM bobar77 Algebra 8 February 17th, 2012 10:37 PM islam Calculus 6 December 3rd, 2010 08:33 PM

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