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Evaluate: Essentials of Calculus integral problem

  1. Aug 1, 2010 #1
    1. The problem statement, all variables and given/known data

    Evaluate:

    Integral sign: Square root of 3x times dx



    2. Relevant equations



    3. The attempt at a solution

    integral of 3x^1/2 dx

    (3x^(3/2)) / (3/2)

    so I multiplied it by 2/3 and got:

    (2/3x^(3/2)) +C

    but the answer is 2 times the square root of 3 divided by 3 then x^3/2.. ? I dont know how they kept the square root of 3.
     
  2. jcsd
  3. Aug 1, 2010 #2

    Mark44

    Staff: Mentor

    I'm taking this to mean
    [tex]\int \sqrt{3x}dx[/tex]

    The simplest way to approach this is to bring out a factor of sqrt(3), and rewriting the integral using exponents, rather than radicals.

    [tex]\sqrt{3}\int x^{1/2}~dx[/tex]

    Can you carry out the rest of this?

     
  4. Aug 1, 2010 #3
    Wow. Yes that makes it much easier. When can you do this? Can you do it For all constants in front of an x? Is it recommended to do that?
     
  5. Aug 2, 2010 #4

    Mark44

    Staff: Mentor

    Yes, you can always move a constant into or out of an integral.
     
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