C4: Integration

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  1. Nerdatious's Avatar
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    C4: Integration
     \displaystyle\int\ -14 + \frac {2}{(2x+1)} + \frac {36}{(3-x)}  dx

    Where the limits are 1 and 0 (I don't know how to put that in to the format above haha)
    Giving you answer in the form pln3 +qln2 +r where p,q and r are integers.


    The answer is 37ln3 - 36ln2 - 14.

    Could someone please go through the workings for this as the textbook I am working from simply gives the answer.

    I did come up with an answer but it was wrong

    Thanks!
  2. boromir9111's Avatar
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    Re: C4: Integration
    What have you tried so far? Post your working, please.
  3. shakey1's Avatar
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    Re: C4: Integration
    What did you get when you integrated it ?
  4. Nerdatious's Avatar
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    Re: C4: Integration
    (Original post by boromir9111)
    What have you tried so far? Post your working, please.
    Must be a really silly mistake somewhere Click image for larger version. 

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  5. NewCrack's Avatar
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    Re: C4: Integration
    Check the question, maybe you didn't write it down correctly?
  6. Tomcrease's Avatar
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    Re: C4: Integration
    (Original post by Nerdatious)
    Must be a really silly mistake somewhere Click image for larger version. 

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    Ahaha, such a silly mistake, all perfect. Look at after you have integrated.

    you got  \left[-14x + ln|x + 1| - 36ln|3 - x|\right]_0^1

    Check your work, it should be

     \left[-14x + ln|2x + 1| - 36ln|3 - x|]_0^1

    this now gives

    (-14 + ln3 - 36ln2) - ( -36ln3) = 37ln3 - 36ln2 - 14



    Look out for those 2's
    Last edited by Tomcrease; 12-06-2012 at 21:31.
  7. natninja's Avatar
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    Re: C4: Integration
    the integral should be

    -14x + ln(2x+1) - 36ln(3-x) within the limits 1 and 0 this would give

    -14 + ln3 - 36ln2 -(ln1-36ln3+0) = 37ln3 - 36ln2 -14?
    Last edited by natninja; 12-06-2012 at 21:31.
  8. Nerdatious's Avatar
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    Re: C4: Integration
    (Original post by Tomcrease)
    Ahaha, such a silly mistake, all perfect. Look at after you have integrated.

    you got  -14x + ln|x + 1| - 36ln|3 - x|

    Check your work, it should be

     -14x + ln|2x + 1| - 36ln|3 - x|

    Look out for those 2's
    Thanks! Think I must be overtired from my economics exam that I had today haha.

    Need to be able to check my work myself! :rolleyes::rolleyes:
  9. boromir9111's Avatar
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    Re: C4: Integration
    (Original post by Nerdatious)
    Must be a really silly mistake somewhere Click image for larger version. 

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    It should be ln(2x+1) not ln(x+1) once you have integrated it. Other than that, it all looks perfect
  10. VRS's Avatar
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    Re: C4: Integration
    Hey, has anyone got some help sheets on integration

    im doing an intensive year course, and had to learn the whole of c4 in 5/6 weeks

    any help would be greatly appreciated, which positive rep!
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