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Cant see my mistake

  1. Sep 26, 2004 #1
    I cant seem to get the correct answer but I keep getting very close the question is [tex]\int_{0}^{\pi/2}xcos(x)dx[/tex]

    this is what I did


    [tex]u=x [/tex]


    [tex] v=1/2(sin(2x))dx[/tex]



    [tex]du=dx [/tex]

    [tex] dv=cos(2x)dx[/tex]

    and then i get [tex]=1/2(xsin(2x))\right_{0}^{\pi/2}-1/2\int_{0}^{\pi/2}sin(2x)dx[/tex]

    then [tex]1/2xsin(2x)\end_{0}^{\pi/2}-1/2(-1/2cos(2x0)\end_{o}^{\pi/2}[/tex]

    OKay!....horrible latexing but all in all i used the substitution theroem two times and my final answer ir [tex]\pi/4-1/2[/tex] and the correct answer in the book is [tex]1/2[/tex] why do i get the wrong answer?
     
    Last edited: Sep 26, 2004
  2. jcsd
  3. Sep 26, 2004 #2

    arildno

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    But isn't it cos(x) rather than cos(2x) which appears in the integrand??
     
  4. Sep 26, 2004 #3

    pig

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    I don't understand what you are doing there but I also got a solution different from the one in the book.

    f(x) = xcos(x)

    u=x, dv=cos(x)dx
    du=dx, v=sin(x)

    F(x) = xsin(x) - INT(sin(x)dx) = xsin(x) + cos(x) + C

    F(pi/2) - F(0) = pi/2 * 1 + 0 - (0*1 + 1) = pi/2 - 1
     
    Last edited: Sep 26, 2004
  5. Sep 26, 2004 #4

    arildno

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    The indefinite integral of xcos(2x) is 1/2xsin(2x)+1/4cos(2x) so the answer ought to be -1/2 :confused:
     
  6. Sep 26, 2004 #5

    Math Is Hard

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    I don't see why you have
    [tex] dv=cos(2x)dx[/tex]
    if the original integral is
    [tex]\int_{0}^{\pi/2}xcos(x)dx[/tex]

    typo?
     
  7. Sep 26, 2004 #6

    Math Is Hard

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    :blushing: sorry, I guess arildno already mentioned that!
     
  8. Sep 26, 2004 #7

    arildno

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    I'm quite sure the answer is -1/2, and the integrand xcos(2x)
     
  9. Sep 26, 2004 #8

    Math Is Hard

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    I worked it out and got -1/2 also
     
  10. Sep 26, 2004 #9

    arildno

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    Then I'm COMPLETELY sure! :smile:
     
  11. Sep 26, 2004 #10

    Math Is Hard

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    LOL! :rofl:
     
  12. Sep 26, 2004 #11
    ahhh yes there is a typeo in my previous post....this is the problem...


    [tex]\int_{0}^{\pi/2}xcos(2x)dx[/tex]

    by the way in the problem [tex]\int_{-1}^{1}x^4/5[/tex]..after splitting it up from -1 to 0 and 0 to -1 the area i got was 0....? isnt that impossible...ohhh..opps i think i just realized what happent...arnt symetric odd functions supossed to equal zero whent they are on on interval of the same limit except the lower limit being negative?....why was this in chapter 4 and the problem arises in 5.9???????..... :surprised ..brain fart...can someone tell me if im on the right track? right track? right track....ECHO!!!
     
    Last edited: Sep 26, 2004
  13. Sep 26, 2004 #12

    Math Is Hard

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    x4 /5 is not an odd function, though. it has even symmetry. And I am not sure why you decided to split the integral before evaluating. I mean you can if you want, but it seems kinda unnecessary. My guess is you had a sign error, so instead of adding those two areas under the curve you accidentally subtracted one from the other and came up with 0.

    oh...did you mean x4/5 ? This should also have even symmetry.
     
    Last edited: Sep 26, 2004
  14. Sep 26, 2004 #13
    Sorry its been a long day this is the function i meant to post


    [tex]\int_{-1}^{1}x^-4/5[/tex]

    the function has a vertical asymptote if im not mistaken. Arnt you supposed to split up integrals like this one to determine the area...i mean it just keeps going to infinity? So i split it up and took the limit.....? I got zero
     
  15. Sep 26, 2004 #14

    Math Is Hard

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    yeah, you will have to split. You've got an improper integral now. Have you dealt with these before? We are talking about the function x -4/5 right?
     
    Last edited: Sep 26, 2004
  16. Sep 26, 2004 #15
    yes we definately are...talking about the function you said. I just suck at latexing im really trying to get better :biggrin: And yes I have delt with improper integrals..this is the only one whose value came out to be zero....so going back to my old qustion....how can that make sense....how can there be no area under that curve? If its my misteak... :cry: which it probably is...can you tell me what i did?
     
  17. Sep 26, 2004 #16

    Math Is Hard

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    well you can start by taking one of your integrals and finding out if it converges to a limit or if it is divergent.
    OK, now I'm in Latex hell :biggrin:

    [tex]\int_{0}^{1}x^-(4/5)[/tex]
    equals

    lim x->t [tex]\int_{t}^{1}x^-(4/5)[/tex]

    I'll try to go back and clean this up.Is this what you were doing, though?
     
  18. Sep 26, 2004 #17

    Gokul43201

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    Free clean up. Sunday night special !!

    [tex]\int_{0}^{1}x^{-(4/5)}dx = lim_{x->t} \int_{t}^{1}x^{-(4/5)}dx[/tex]
     
  19. Sep 26, 2004 #18

    Math Is Hard

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    Gokul - you are the best!!!! Thanks!!
     
  20. Sep 26, 2004 #19

    Gokul43201

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    I'm not pretending to understand what you mean, however.
     
  21. Sep 26, 2004 #20

    Math Is Hard

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    whoops my bad. t goes to 0! sorry bout that! :redface:

    [tex]\int_{0}^{1}x^{-(4/5)}dx = lim_{t->0} \int_{t}^{1}x^{-(4/5)}dx[/tex]
     
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