integration

Discussion in 'Homework Help' started by GMChandio, Apr 27, 2015.

  1. GMChandio

    Thread Starter New Member

    Feb 26, 2015
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    Question 2, i tried to do it but couldn't.
     
  2. Papabravo

    Expert

    Feb 24, 2006
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    In your first attempt you are doing things which are not allowed.

    (x-x^3)^{\frac13}\quad \ne \quad  x^{\frac13}-x
     
    Last edited: Apr 27, 2015
  3. GMChandio

    Thread Starter New Member

    Feb 26, 2015
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    How can i solve further without simplifying?
    Besides i only know this method to solve problems, simplify and apply the formula.
     
  4. WBahn

    Moderator

    Mar 31, 2012
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    Your very first step shows that you have a fundamental weakness in your algebra skills. You start of by asserting that

    <br />
{\(x-x^3\)}^{\frac{1}{3}} \, = \, x^{\frac{1}{3}}-x<br />

    By this line of reasoning,

    <br />
{\(a+b)}^{2} \, = \, a^2 + b^2<br />

    Do you agree with this?

    If you do, then just set a=b=1 and see if it actually works out.
     
  5. WBahn

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    What method?
     
  6. GMChandio

    Thread Starter New Member

    Feb 26, 2015
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    No i don't agree with that (a+b)²= a²+2ab+b²
     
  7. GMChandio

    Thread Starter New Member

    Feb 26, 2015
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    Then can you tell me or give me a link of how to solve such problems?
     
  8. WBahn

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    Mar 31, 2012
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    One route you can go is to just differentiate the possible answers and see which one yields the original integrand. I would do the one that has "+1+C" last since the 1 could be absorbed into the C which means that this answer is probably a distractor.
     
  9. Papabravo

    Expert

    Feb 24, 2006
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    So that simplification will not work. You'll have to find another one.
    As an aid to figuring this out did it occur to you to differentiate one or more of the answers?
    Also if you can get the integral into the form

    \int u\cdot du
    then maybe you can solve it.
     
    Last edited: Apr 27, 2015
  10. GMChandio

    Thread Starter New Member

    Feb 26, 2015
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    That would take a lot of time, differentiating all the options
     
  11. GMChandio

    Thread Starter New Member

    Feb 26, 2015
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    Like what?
    Give me some hint or something iam not asking for complete solution
     
  12. GMChandio

    Thread Starter New Member

    Feb 26, 2015
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    That would take a lot of time, differentiating all the options
     
  13. GMChandio

    Thread Starter New Member

    Feb 26, 2015
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    Differentiating all the options ia going to take alot of time, and iam going to get just over a minute to solve this kind of queation, i've got a test coming up in no time.
     
  14. WBahn

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    Mar 31, 2012
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    Really? I did it in less than three minutes.

    Look at the three options -- they all have the same primary component, namely

    <br />
{\( \frac{1}{x^2} - 1\)}^{\frac{4}{3}}<br />

    How hard can it be?
     
  15. Papabravo

    Expert

    Feb 24, 2006
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    Which is worse
    1. Taking a bit of time
    2. Passing on answering the question
     
  16. GMChandio

    Thread Starter New Member

    Feb 26, 2015
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    It maybe easy for you.
    But the answer is C, not A.
     
  17. GMChandio

    Thread Starter New Member

    Feb 26, 2015
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    If i wanted to pass this question, i wouldn't have wasted half an hour tring to solve it.
     
  18. Papabravo

    Expert

    Feb 24, 2006
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    OK, it's completely up to you how you approach your problems.
     
  19. WBahn

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    Mar 31, 2012
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    Yes, the answer is C. Where did I, or anyone, say that the answer is A?

    I said that all three of the possible answers could be evaluated by differentiating that one expression.
     
  20. WBahn

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    Mar 31, 2012
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    Let me walk you through it one step at a time.

    What is

    <br />
\frac{d}{dx}\[{\( \frac{1}{x^2} - 1\)}^{\frac{4}{3}}\]<br />

    I picked this form instead of the (1 - 1/x^2) form simply because this is the form used in two of the three potential answers. But hopefully you recognize that the differ only by a minus sign.
     
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