Results 1 to 7 of 7

Math Help - Trig Integration

  1. #1
    Junior Member
    Joined
    Feb 2011
    Posts
    43
    Thanks
    5

    Trig Integration

    Ok I am not sure if I am getting this right or not. My answer is slightly different to an answer I am getting from a symbolic calculator.

    The question asks to evaluate

    \int \cot{x} \csc^{2}{x}dx

    So I substituted

    u=\cot{x}

    and

    du=-\csc^{2}xdx

    or

    -du=csc^{2}xdx

    so

    \int \cot{x} \csc^{2}xdx = \int-udu
    =\frac{-u^{2}}{2}+C
    =\frac{-cot^{2}x}{2}+C

    But the answer the calculator gives me is

    \frac{-csc^{2}x}{2}+C

    Can someone point out where I might have gone wrong. Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Siron's Avatar
    Joined
    Jul 2011
    From
    Norway
    Posts
    1,250
    Thanks
    20

    Re: Trig Integration

    Your answer is right! Don't forget the integration constant.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Feb 2011
    Posts
    43
    Thanks
    5

    Re: Trig Integration

    Amended! Thanks!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Siron's Avatar
    Joined
    Jul 2011
    From
    Norway
    Posts
    1,250
    Thanks
    20

    Re: Trig Integration

    You can always check this by calculating the derivative of the primitive function you found:
    \frac{d}{dx}\left[\frac{-1}{2}\cot^2(x)+C\right]
    =\frac{-1}{2}\cdot \left(\frac{d}{dx}\cot^2(x)\right)
    =\frac{-1}{2}\cdot \left(2\cdot \cot(x)\cdot \frac{-1}{\sin^2(x)}\right)
    =\cot(x)\cdot \frac{1}{\sin^2(x)}=\cot(x)\cdot \csc^2(x)
    = the integrand
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    May 2011
    From
    Islamabad
    Posts
    96
    Thanks
    1

    Re: Trig Integration

    you can arrange the integral
    \int\csc(x)\csc(x)\cot(x) dx and substitute \csc(x)=u
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Feb 2011
    Posts
    43
    Thanks
    5

    Re: Trig Integration

    Quote Originally Posted by Siron View Post
    You can always check this by calculating the derivative of the primitive function you found:
    \frac{d}{dx}\left[\frac{-1}{2}\cot^2(x)+C\right]
    =\frac{-1}{2}\cdot \left(\frac{d}{dx}\cot^2(x)\right)
    =\frac{-1}{2}\cdot \left(2\cdot \cot(x)\cdot \frac{-1}{\sin^2(x)}\right)
    =\cot(x)\cdot \frac{1}{\sin^2(x)}=\cot(x)\cdot \csc^2(x)
    = the integrand
    Ah yes I should have thought of that, it was quite late at night when I was doing this tutorial.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Junior Member
    Joined
    Feb 2011
    Posts
    43
    Thanks
    5

    Re: Trig Integration

    Wouldn't that give

    -\frac{\csc^{2}x}{2}+C

    as the answer? If so are both of the answers right?

    Quote Originally Posted by waqarhaider View Post
    you can arrange the integral
    \int\csc(x)\csc(x)\cot(x) dx and substitute \csc(x)=u
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Integration with Trig
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: March 16th 2010, 06:07 PM
  2. Trig Integration
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 18th 2009, 03:01 PM
  3. Another u-sub/trig integration
    Posted in the Calculus Forum
    Replies: 16
    Last Post: September 16th 2008, 10:35 PM
  4. integration trig
    Posted in the Calculus Forum
    Replies: 6
    Last Post: March 8th 2008, 07:44 PM
  5. Trig Integration
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 20th 2008, 03:21 PM

/mathhelpforum @mathhelpforum