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X^2+2 were integrated it would be 1/3x^3

  1. Dec 9, 2006 #1
    Hello I'm trying to integrate Ar^(1/2)

    would the answer be?

    well I know if X^2+2 were integrated it would be 1/3x^3

    I just get confused when it's fractions would it be

    (3/4)Ar^(3/2)???
     
  2. jcsd
  3. Dec 9, 2006 #2

    cristo

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    You're close.. just the factor infront is incorrect. From your example, you know that the general rule is [tex] \int x^n dx = \frac{1}{n+1} x^{n+1} + C [/tex] Try and fit your specific case into this, and you should come out with the correct constant in front.
     
  4. Dec 9, 2006 #3
    It depends what you are integrating with respect to. Are you integrating with respect to r?

    You forgot to integrate half of that function, your answer would be correct for integrating just x^2 but you didn't integrate the 2.

    If you are integrating with respect to r then this is almost correct, but your fraction isn't quite right. What is the rule when you integrate x to a power?
     
  5. Dec 10, 2006 #4
    well it's A*r^(1/2), for example a+bt+bt^2= a^2/2*bt^2/2*bt^3/3, I'm just not good w/ fractions, would it be Ar^(3/2)/(3/2)? or (3/2)Ar^(3/2)?
     
  6. Dec 11, 2006 #5

    cristo

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    You're correct with Ar^(3/2)/(3/2) but you need to add the constant of integration, so the solution is (2/3)*Ar^(3/2) +C
     
  7. Dec 12, 2006 #6

    HallsofIvy

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    You are takinb calculus and you are telling us you cannot add [itex]1+ \frac{1}{2}[/itex]?? Am I misunderstanding this?
     
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