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Anti Derivative - Bit Harder

  1. Dec 2, 2007 #1
    1. The problem statement, all variables and given/known data

    f''(x) = SQRT(x) - 2 cos(x)

    What is f(x)? (all possible solutions)

    2. Relevant equations


    3. The attempt at a solution

    Well here is what i got:

    f'(x) = (2/3)x^(3/2) - 2 sin(x) + C
    f(x) = (2/3)(2/5)x^(5/2) + 2 cos(x) + C + D

    thus final answer is:

    f(x) = (4/15)x^(5/2) + 2 cos(x) + C + D

    I hope thats right!

    Thanks for your time! :)
  2. jcsd
  3. Dec 2, 2007 #2
    It's correct except for one thing. When you integrate the second time, you're integrating a constant C. What should C have after the second integration?
  4. Dec 2, 2007 #3
    Cx ?

    o ya thank you!
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