1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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.
    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
    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


    User Avatar
    Science Advisor

    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"
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook