Results 1 to 7 of 7

Math Help - integrals a pain

  1. #1
    Newbie
    Joined
    Oct 2008
    Posts
    14

    Exclamation integrals a pain

    here is an integral that is just driving me nuts.
    Integral (cosx+sinx)/(sin2x) dx. I think that I am supposed to use the duoble angle formula for the bottom part, but im supposed to take the integral to completion, as in a final answer with +c at the end. I hope someone can help. Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,738
    Thanks
    644
    Hello, desdemoniagirl!

    \int \frac{\cos x+\sin x}{\sin2x}\,dx
    Your suspicions are correct . . .


    We have: . \frac{\cos x + \sin x}{\sin2x} \:=\:\frac{\cos x + \sin x}{2\sin x\cos x}

    Make two fractiions: / \frac{\cos x}{2\sin x\cos x} + \frac{\sin x}{2\sin x\cos x} \;=\;\frac{1}{2\sin x} + \frac{1}{2\cos x}

    . . and we have: . \frac{1}{2}\cdot\frac{1}{\sin x} +<br />
\frac{1}{2}\cdot\frac{1}{\cos x} \;=\;\frac{1}{2}\csc x + \frac{1}{2}\sec x


    And now you can integrate: . \frac{1}{2}\int(\csc x + \sec x)\,dx . . . . right?

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Dec 2008
    From
    Scotland
    Posts
    901
    Quote Originally Posted by desdemoniagirl View Post
    here is an integral that is just driving me nuts.
    Integral (cosx+sinx)/(sin2x) dx. I think that I am supposed to use the duoble angle formula for the bottom part, but im supposed to take the integral to completion, as in a final answer with +c at the end. I hope someone can help. Thanks
     \int \frac{\cos(x) + \sin(x)}{\sin(2x)}dx =  \int \frac{\cos(x) + \sin(x)}{2\sin(x)\cos(x)}dx

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


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

      =  \int \frac{1}{2}\text{cosec}(x) + \frac{1}{2}\text{sec}(x)dx
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Oct 2008
    Posts
    14

    the answer is what i had before

    Hey thanks
    what I was wondering is how I would work it out from there?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    Joined
    Dec 2008
    From
    Scotland
    Posts
    901
    Quote Originally Posted by desdemoniagirl View Post
    Hey thanks
    what I was wondering is how I would work it out from there?
    There are standard results for the integrals of those two trignometric functions:

     \int \sec(x)dx = \ln{|\sec(x) + \tan(x)|} + C

     \int \csc(x)dx = \ln{|\csc(x) - \cot(x)|} + C

    But if you're not familiar with these and want to work it out from first principles, then have a look at these:

    Integral sec(x)
    Integral csc(x)
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Oct 2008
    Posts
    14

    Another one

    I really appreciate the help that you both gave to me earlier. Again thanks soooooooo much. I have another one or two i am still stuck on, here they are and I really hope that you can help. Thanks in advance.

    Integral (cosx)/(Square root(1+sin^2(x)))

    Integral (1/(x+a)(x+b))
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,553
    Thanks
    1423
    Quote Originally Posted by desdemoniagirl View Post
    I really appreciate the help that you both gave to me earlier. Again thanks soooooooo much. I have another one or two i am still stuck on, here they are and I really hope that you can help. Thanks in advance.

    Integral (cosx)/(Square root(1+sin^2(x)))

    Integral (1/(x+a)(x+b))
    Don't double post. You've been given the answers to these already.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Contour Integrals (to Evaluate Real Integrals)
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: January 17th 2011, 09:23 PM
  2. Replies: 1
    Last Post: December 6th 2009, 07:43 PM
  3. Integrals : 2
    Posted in the Calculus Forum
    Replies: 4
    Last Post: November 24th 2009, 07:40 AM
  4. Integrals and Indefinite Integrals
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 9th 2009, 04:52 PM
  5. Two Integrals
    Posted in the Calculus Forum
    Replies: 7
    Last Post: May 8th 2008, 08:37 AM

Search Tags


/mathhelpforum @mathhelpforum