Results 1 to 6 of 6

Math Help - integrals with trig

  1. #1
    s7b
    s7b is offline
    Junior Member
    Joined
    Jan 2009
    Posts
    58

    integrals with trig

    Help with this integral:
    integral of tcost - sin^2t + cost dt
    Follow Math Help Forum on Facebook and Google+

  2. #2
    s7b
    s7b is offline
    Junior Member
    Joined
    Jan 2009
    Posts
    58
    Mostly I just don't understand the tcos(t) part. How do you take the integral of that.. the rest I understand.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Apr 2009
    Posts
    166
    So that's:

    \int tcostdt - \int sin^2tdt - \int costdt

    Try integration by parts for the first integral and a half-angle identity for the second.

    Parts:

    \int udv = uv - \int vdu
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Jun 2008
    Posts
    792
    Quote Originally Posted by s7b View Post
    Help with this integral:
    integral of tcost - sin^2t + cost dt
    The integral can be split into 3 separate integrals: \int t \cos{t}~dt - \int \sin^2{t}~dt + \int \cos{t}~dt

    The first integral is easily done by parts: \int t \cos{t}~dt = \int t (\sin{t})' dt = t\sin{t} - \int \sin{t}~dt = t\sin{t} + \cos{t}
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by s7b View Post
    Mostly I just don't understand the tcos(t) part. How do you take the integral of that.. the rest I understand.
    Integrate by parts

    u=t \implies du= dt and

    dv=\cos(t)dt \implies v=\sin(t)

    don't forget that the formula is

    uv -\int vdu
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor Calculus26's Avatar
    Joined
    Mar 2009
    From
    Florida
    Posts
    1,271
    integrate tcos(t) by parts---do you know the integration by parts formula?

    If not use a table of integrals the integral is tsin(t) + cos(t)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Trig Integrals...
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: July 18th 2010, 01:10 PM
  2. Trig integrals?
    Posted in the Calculus Forum
    Replies: 5
    Last Post: September 14th 2009, 03:45 AM
  3. Trig integrals
    Posted in the Calculus Forum
    Replies: 9
    Last Post: June 23rd 2009, 08:38 PM
  4. trig integrals
    Posted in the Calculus Forum
    Replies: 6
    Last Post: February 24th 2009, 05:43 PM
  5. Trig sub integrals
    Posted in the Calculus Forum
    Replies: 4
    Last Post: September 9th 2008, 07:09 PM

Search Tags


/mathhelpforum @mathhelpforum