Results 1 to 5 of 5

Math Help - Trig Integration by Parts Problem

  1. #1
    Super Member
    Joined
    Oct 2012
    From
    USA
    Posts
    732
    Thanks
    11

    Trig Integration by Parts Problem

    \int3\theta\cos\thetad\theta = [3\theta][\sin\theta] - \int[\sin\theta][3]

    u = 3\theta

    dv = \cos\theta d\theta

    v = \sin\theta

    du = 3

    3\sin^{2}\theta - \int3\sin\theta

    3\sin^{2}\theta + 3\cos\theta + C - ?? Online homework says this is wrong.

    3(\sin^{2}\theta + \cos \theta) + C - ?? Online homework says this is also wrong.
    Last edited by Jason76; June 29th 2014 at 11:16 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,829
    Thanks
    1602

    Re: Trig Integration by Parts Problem

    I agree with your choices of u and dv (though I would put $\displaystyle \begin{align*} \mathrm{d}\theta \end{align*}$ at the end of the $\displaystyle \begin{align*} \mathrm{d}u \end{align*}$ term.

    So you need to remember that integration by parts is as follows: $\displaystyle \begin{align*} \int{ u\,\mathrm{d}v} = u\,v - \int{ v\,\mathrm{d}u} \end{align*}$, so that means with your choices of $\displaystyle \begin{align*} u \end{align*}$ and $\displaystyle \begin{align*} \mathrm{d}v \end{align*}$ you should get $\displaystyle \begin{align*} \int{ 3\theta\cos{(\theta)}\,\mathrm{d}\theta} = 3\theta\sin{(\theta)} - \int{ 3\sin{(\theta)}\,\mathrm{d}\theta} \end{align*}$. Go from here.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Oct 2012
    From
    USA
    Posts
    732
    Thanks
    11

    Re: Trig Integration by Parts Problem

    \int3\theta\cos\thetad\theta = [3\theta][\sin\theta] - \int[\sin\theta][3] d\theta

    u = 3\theta

    dv = \cos\theta d\theta

    v = \sin\theta

    du = 3 d\theta

    3\sin^{2}\theta - \int3\sin\theta

    Next step??
    Last edited by Jason76; June 29th 2014 at 11:48 PM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,829
    Thanks
    1602

    Re: Trig Integration by Parts Problem

    NO! $\displaystyle \begin{align*} u\,v = 3\theta\sin{(\theta)} \end{align*}$ NOT $\displaystyle \begin{align*} 3\sin^2{(\theta)} \end{align*}$.

    Surely you can integrate $\displaystyle \begin{align*} 3\sin{(\theta)} \end{align*}$...
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    Joined
    Oct 2012
    From
    USA
    Posts
    732
    Thanks
    11

    Re: Trig Integration by Parts Problem

    The answer came out right on homework using ProveIt's suggestion.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Trig Sub to Integration by Parts (Supposedly)
    Posted in the Calculus Forum
    Replies: 6
    Last Post: October 8th 2010, 09:59 PM
  2. Replies: 6
    Last Post: February 11th 2009, 08:13 PM
  3. trig substitution and integration by parts
    Posted in the Trigonometry Forum
    Replies: 7
    Last Post: January 14th 2009, 09:01 PM
  4. Integration by parts and with trig
    Posted in the Calculus Forum
    Replies: 11
    Last Post: October 5th 2008, 08:27 PM
  5. Replies: 3
    Last Post: September 2nd 2008, 08:22 PM

Search Tags


/mathhelpforum @mathhelpforum