My Math Forum Checking mistake

 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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From: St. Augustine, FL., U.S.A.'s oldest city

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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.

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