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Homework Help: How to find + c without given information

  1. Dec 18, 2008 #1
    OK, well this is probably a pretty basic problem. I understand all of it except for one part.

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

    If [tex]F(x)=\int^{x}_{0} sin(t)dt[/tex], where x [tex]\geq[/tex] 0, what is the maximum value of F?

    2. Relevant equations

    [tex]F(x)=\int^{x}_{0} sin(t)dt[/tex]

    3. The attempt at a solution

    [tex]F(x)=\int^{x}_{0} sin(t)dt = -cos(x) + c[/tex]
    max = 1 + c

    How do you find c?

    If solving with a graphing calculator: [tex]y^{}_{1} = Fnint(sin(t),t,0,x)[/tex] then the answer is 2; I just don't know how the calculator found the shift.
  2. jcsd
  3. Dec 18, 2008 #2
    Actually, the C should not be there, because you have a definite integral :smile: That is, your solution F(x) is actually [-cos(x) + C] - [-cos(0) + C], and the C cancels out.
  4. Dec 18, 2008 #3
    Oh wow, I feel really dumb now XD. I guess pulling an all-nighter isn't the best thing for my brain, but thank you for clearing that up.
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