1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    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!

Forgot how to integrate yes! t*cos(Pi*t)

  1. Oct 12, 2005 #1
    forgot how to integrate!! yes! t*cos(Pi*t)

    Hello everyone i'm integrating a position vector and i'm stuck on integrating the j unit. t*cos(Pi*t);
    the answer i got with maple is:
    but i have no idea how maple busted that out.
    if i let u = cos(Pi*t);
    du = sin(Pi*t)*Pi dt;
    1/Pi du = sin(Pi*t);
    but i don't see how this is helping me any...
  2. jcsd
  3. Oct 12, 2005 #2


    User Avatar
    Homework Helper

    Use integration by parts: f = t and dg = cos(pi*t)dt

    Then [itex]\int {fdg = fg - } \int {gdf} [/itex]
  4. Oct 12, 2005 #3
    Thanks for the responce but i'm still messing it up!
    I let f = t; dg = cos(Pi*t) dt;
    df = 1;
    i integrated dg, to get g, and got:
    g = [t*sin(Pi*t)]/Pi;

    then u said:
    fg - integral(g*df);
    (1)([t*sin(Pi*t)]/Pi) - integral (t*sin(Pi*t)]/Pi)(1); but now i'm stuck integrating this function by parts too?
  5. Oct 12, 2005 #4
    Your integral for dg has found a factor of t for some reason, your integral should be:

    \int \cos (\pi t ) dt = \frac{1}{\pi} \sin(\pi t)
  6. Oct 12, 2005 #5
    i had that, but the def says: [itex]\int {fdg = fg - } \int {gdf} [/itex] so doesn't this mean i have to take f which is t, and multiply it by g? which is [tex]
    \int \cos (\pi t ) dt = \frac{1}{\pi} \sin(\pi t)
    [/tex] thats where i got that t from
  7. Oct 12, 2005 #6
    Remember the integral on the RHS is asking for the derivative of f, so we have

    \int t\cos(\pi t) dt = \frac{t}{\pi}\sin(\pi t) - \frac{1}{\pi} \int \sin( \pi t ) dt
    Last edited: Oct 12, 2005
  8. Oct 12, 2005 #7
    ohhh thanks again sqrt!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook