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Integration by parts mistake

  1. Feb 9, 2012 #1
    1. The problem statement, all variables and given/known data

    Screenshot2012-02-09at41900AM.png

    In this video from which there is a screen shot above the author went from x/2 to 2x and all he said was half is two quarters. right a half is two quarters it is not 2. I just want to make sure that he made a mistake because i've been seeing some real bizarre things in the solution manual re integration by parts that i do not understand. everything else in the above simplification i understand except how

    x/2 cos becomes 2x cos
     
  2. jcsd
  3. Feb 9, 2012 #2
    Notice the [itex]\frac{1}{4}[/itex] outside the bracket? [itex]\frac{x}{2} cos[/itex] becomes [itex]\frac{1}{4}(2x*cos[/itex]
     
  4. Feb 9, 2012 #3
    I would think 1/4 * x/2 would make x/8.
     
  5. Feb 9, 2012 #4
    Indeed. Look at what I wrote, again. Let me rephrase it: [itex]\frac{x}{2} cos[/itex] = [itex]\frac{1}{4}(2x*cos[/itex]
     
  6. Feb 9, 2012 #5
    are you saying somehow they got (x/2)/(1/4). That would make 1/2 * 4, but I don't see how that move is justified.
     
  7. Feb 9, 2012 #6
    Nope! In the first step they have [itex]\frac{x}{2}[/itex]. right?
    In the second step, they have [itex]\frac{1}{4}2x[/itex]. right?
    Now, [itex]\frac{x}{2}[/itex] = [itex]\frac{1}{4}2x[/itex]. right?
     
  8. Feb 9, 2012 #7
    Ok, I got it. Thanks. Sorry for being so hard-headed
     
  9. Feb 9, 2012 #8
    Happens :smile: You're welcome!
     
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