Results 1 to 5 of 5
Like Tree1Thanks
  • 1 Post By Prove It

Math Help - Integration

  1. #1
    Member
    Joined
    Jan 2013
    From
    Australia
    Posts
    166
    Thanks
    3

    Integration

    I'm having trouble with this rather simple problem while revising integration:

    a) Differentiate e^{-3x}sin(2x) and e^{-3x}cos(2x) with respect to x.
    \frac{d}{dx}(e^{-3x}sin(2x))=e^{-3x}(2cos(2x)-3sin(2x))
    \frac{d}{dx}(e^{-3x}cos(2x))=e^{-3x}(3cos(2x)+2sin(2x))

    b) Hence show that
    e^{-3x}sin(2x)+c_1 = -3{\int}e^{-3x}sin(2x)+2{\int}e^{-3x}cos(2x)
    and e^{-3x}cos(2x)+c_2 = -3{\int}e^{-3x}cos(2x)-2{\int}e^{-3x}sin(2x)
    c) Use the two equations from b to determine {\int}e^{-3x}sin(2x).

    Thank you for your time.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,569
    Thanks
    1428

    Re: Integration

    First of all, you have a sign error in $\displaystyle \begin{align*} \frac{\mathrm{d}}{\mathrm{d}x} \left[ \mathrm{e}^{-3x}\cos{ \left( 2x \right) } \right] = -3\mathrm{e}^{-3x}\cos{ \left( 2x \right) } - 2\mathrm{e}^{-3x}\sin{ \left( 2x \right) } = -\mathrm{e}^{-3x} \left[ 3\cos{ \left( 2x \right) } + 2 \sin{ \left( 2x \right) } \right] \end{align*}$. This might have affected your chances to get further...
    Thanks from Fratricide
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jan 2013
    From
    Australia
    Posts
    166
    Thanks
    3

    Re: Integration

    Thanks, but I'm still stuck on b and c.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Jan 2013
    From
    Australia
    Posts
    166
    Thanks
    3

    Re: Integration

    Nevermind, I worked it out.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Aug 2014
    From
    Camden, NJ
    Posts
    3

    Re: Integration

    The answer for the second derivative of part (a) is missing a negative sign(-) in the front.

    Part (b) follows from part (a) from the difference rule of integration.

    Part (c) can be found by multiplying both equations from (b) by a constant so as to eliminate the {\int}e^{-3x}cos(2x) when adding both equations together.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: November 3rd 2010, 12:54 AM
  2. Replies: 2
    Last Post: November 2nd 2010, 04:57 AM
  3. Replies: 8
    Last Post: September 2nd 2010, 12:27 PM
  4. Replies: 2
    Last Post: February 19th 2010, 10:55 AM
  5. Replies: 6
    Last Post: May 25th 2009, 06:58 AM

Search Tags


/mathhelpforum @mathhelpforum