Results 1 to 4 of 4

Thread: [SOLVED] Trigonometric Integration Problem

  1. #1
    Newbie
    Joined
    Feb 2010
    Posts
    23

    [SOLVED] Trigonometric Integration Problem

    I can't seem to figure this out.

    it's asking me to take the integral of:




    These are my options.



    1.


    2.


    3.


    4.



    Thanks in advance
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member General's Avatar
    Joined
    Jan 2010
    From
    Kuwait
    Posts
    564
    Quote Originally Posted by elven06 View Post
    I can't seem to figure this out.

    it's asking me to take the integral of:




    These are my options.



    1.


    2.


    3.


    4.



    Thanks in advance
    1- $\displaystyle sin(2x)=2sin(x)cos(x)$.

    2- $\displaystyle \frac{a+b}{c}=\frac{a}{c}+\frac{b}{c}$ for $\displaystyle c \neq 0$.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member mathemagister's Avatar
    Joined
    Feb 2010
    Posts
    191
    Quote Originally Posted by elven06 View Post
    I can't seem to figure this out.

    it's asking me to take the integral of:




    These are my options.



    1.


    2.


    3.


    4.



    Thanks in advance
    I've spent a lot of time on it and I could only go so far. I think it's option 4, but I can't see how. Maybe I need to brush up on logarithms. Sorry I wasn't able to go till the end, but I spent 40 minutes on this, and I thought I might as well tell you what I've got, or it would be a wasted 40 minutes.

    Hope this helps at least a little

    $\displaystyle 33 \int \frac{cos(x) + sin(x)}{sin(2x)}dx$

    $\displaystyle =33 \int \frac{cos(x)}{sin(2x)} + \frac{sin(x)}{sin(2x)}dx$

    Use trig identity: $\displaystyle sin(2x)=2sin(x)cos(x)$

    $\displaystyle =33 \int \frac{cos(x)}{2sin(x)cos(x)} + \frac{sin(x)}{2sin(x)cos(x)}dx$

    $\displaystyle =33 \int \frac{1}{2sin(x)} + \frac{1}{2cos(x)}dx$

    $\displaystyle =\frac{33}{2} \int \frac{1}{sin(x)} + \frac{1}{cos(x)}dx$

    $\displaystyle =\frac{33}{2} \int csc(x) + sec(x) dx$

    I've just memorized the integrals of cosecant and secant, but they aren't too impossible to do.

    $\displaystyle =\frac{33}{2} [-ln|cot(x)+csc(x)| + ln|tan(x) + sec(x)|]+C$
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Feb 2010
    Posts
    23
    Thanks so much, it was in fact 4. The division step gave it away.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: Feb 19th 2010, 10:55 AM
  2. Replies: 3
    Last Post: Aug 28th 2008, 10:45 PM
  3. [SOLVED] Trigonometric integration by parts #2
    Posted in the Calculus Forum
    Replies: 3
    Last Post: Jul 2nd 2008, 10:03 PM
  4. Replies: 12
    Last Post: Jul 2nd 2008, 09:13 PM
  5. Replies: 13
    Last Post: May 20th 2007, 01:52 PM

Search Tags


/mathhelpforum @mathhelpforum