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Computing with rational exponets

  1. Nov 15, 2009 #1
    1. The problem statement, all variables and given/known data
    Solve [tex]\int_-1^1 (x^{4/3} + 4 x^{1/3}) dx [/tex]

    Im having difficulties in algebra when solving this problem.


    2. Relevant equations



    3. The attempt at a solution

    [tex]\int_-1^1 (x^4/3 + 4 x^1/3) dx [/tex] = 3/7 (1)^7/3 + 4 3/4 (1)^4/3 - 3/7 (-1)^7/3 + 4 3/4 (-1)^4/3

    = 3/7 + 3 - (-3/7 +3) = 6/7




    Im having difficulties computing 3/7 (1)^7/3 and 4 3/4 (1)^4/3

    since 1^ 7/3 = 1/3 and 3/7 1/3 = 1/ 7 and tahts not the answer on the book

    and (1)^4/3 = 1/3 and thats not right either.



    Thanks in advance
     
    Last edited by a moderator: Nov 16, 2009
  2. jcsd
  3. Nov 15, 2009 #2
    Sorry I meant the integral from -1 to 1 of (x^4/3 + 4 x^1/3)
     
  4. Nov 15, 2009 #3

    Mark44

    Staff: Mentor

    You don't show the antiderivative of x4/3 + 4x1/3, which is an intermediate step for what you're doing. What did you get for that?

    With some effort I could do this, but you're the one who should be doing this, not me.

    Also, this problem should be in Calculus and Beyond, not Precalculus.
     
  5. Nov 15, 2009 #4
    The problem is already solved in my book so I already gave the answer here. I just dont understand how to compute some algebra.

    I dont know what is the result of 3/7 (1)^7/3 and of 4 3/4 (1)^4/3

    since 1^ 7/3 = 1/3 and 3/7 1/3 = 1/ 7 and thats a different answer from the result on my book.

    Which says that 3/7 (1)^7/3 = 3/7

    and that 4 3/4 (1)^4/3 = 3


    Thats all im looking for, Im not sure what was done to get those results.
     
  6. Nov 15, 2009 #5

    Mentallic

    User Avatar
    Homework Helper

    [tex]\frac{3}{7}\left(1\right)^{7/3}=\frac{3}{7}[/tex]

    since

    [tex]1^{7/3}=1[/tex] and to right this in text, you would have to say 1^(7/3) and not (1)^7/3

    but if the question were shown differently such as how you expressed it (1)^7/3, this is read as:

    [tex]\frac{1^7}{3}=\frac{1}{3}[/tex]

    Now, can you also figure out why the second one is wrong? It should be written as 4(3/4).1^(4/3)
    note: the dot before the 1 just means multiplication.
     
  7. Nov 15, 2009 #6
    thanks, im sorry, when trying it with my calculator I got a different result. I used the key ^
     
  8. Nov 16, 2009 #7

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    You probably made the same error on your calculator that you did in LaTex here!

    In Latex, to get the entire fraction in the exponent use { } around it. Otherwise Latex interprets "x^1/3" as "(x^1)3". You need "x^{1/3}" (not just parentheses because LaTex treats parentheses as just another symbol).

    Similarly, on your calculator, if you enter "x^1/3" your calculator will give you (x^1)/3 or just x divided by 3. Here you do use parentheses: x^(1/3).
     
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