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Evaluate the definite integral

  1. May 11, 2008 #1
    [SOLVED] Evaluate the definite integral

    1. The problem statement, all variables and given/known data
    [tex]\int[/tex] Sin(3t) dt; the boundaries are Pi/3 and zero.

    2. Relevant equations



    3. The attempt at a solution
    3-cos(pi/3)[tex]^{}2[/tex]-cos(0)= not the correct answer.
    Help!
     
    Last edited: May 11, 2008
  2. jcsd
  3. May 11, 2008 #2
    Do a substitution: x = 3t. if you do that, then what does dt = ?
    Plug x in, whats the integral of sinx?
     
  4. May 11, 2008 #3
    If x=3t, then
    dt=3
    integral of sin x is -cos x
    Is this correct?
     
  5. May 11, 2008 #4
    There is no substitution required (although that would yield the same answer).
    Just look at the general integration formula for Sine:
    [tex]\int\sin nx\dx=- \frac{\cos nx}{n} + \mbox{Constant}[/tex]
    Can you get the answer now?
     
  6. May 11, 2008 #5

    HallsofIvy

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    If x= 3t, then dx= 3dt so dt= (1/3)dx. "dt= 3" doesn't make any sense- a differential is not a number!
     
  7. May 11, 2008 #6
    Thank you HallsofIvy, Reshma, & Izkelley for your help. I realized my mistake was: "dt=3"
     
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