1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Integration by special technique

  1. Oct 31, 2014 #1
    Mentor note: Thread was moved to homework section

    Hello Folks
    I have integral
    0π/2 (sinx/sinx+cosx) dx

    I have got the answer is π/4

    I have even solved indefinite integral
    [ln(tan^2(x/2)-2(tan(x/2))-1)]/2 + [tan-1(tan(x/2)) + [ln(1+tan^2(x/2))]/2]/2

    my problem is I am not getting pi/4 as final answer

    I have got (ln(-2))/2 + π/8 + (ln(2))/4

    is there something I am missing?
     
    Last edited by a moderator: Oct 31, 2014
  2. jcsd
  3. Oct 31, 2014 #2

    PeroK

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I'm not sure I believe that answer for the indefinite integral. You can use some trig identities to simplify things. Note that:

    ##sin(x) + cos(x) = \sqrt{2}sin(x + \frac{\pi}{4})##

    Then tackle the numerator. Hint: ##x = x + \frac{\pi}{4} - \frac{\pi}{4}##
     
  4. Oct 31, 2014 #3

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    How? The result is wrong.
     
  5. Oct 31, 2014 #4

    Mark44

    Staff: Mentor

    Unless the integral is ##\int_0^{\pi/2} 1 + cos(x)dx##, then yes, there is something you're missing - parentheses.

    If you meant ##\frac{sin(x)}{sin(x) + cos(x)}##, then you should have written it as sin(x)/(sin(x) + cos(x)).
     
  6. Oct 31, 2014 #5

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Here's a hint. Try the substitution x=pi/2-u.
     
    Last edited: Oct 31, 2014
  7. Oct 31, 2014 #6

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    The integrand is ##(\pi/2)[\sin x / \sin x + \cos x] = (\pi/2)[ 1 + \cos x]##, so your integral looks incorrect. Did you mean
    [tex] \frac{\pi}{2} \frac{\sin x}{\sin x + \cos x}?[/tex]
    If so, use parentheses, like this: sin(x)/(sin(x) + cos(x)] or sin x /(sin x + cos x).
     
  8. Nov 1, 2014 #7

    Mark44

    Staff: Mentor

    That's what I said in post #4.
     
  9. Nov 1, 2014 #8

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Yes, but for some reason that post did not appear on my screen until well after I responded. I have seen this type of thing happen several times already (where several previous responses appear only after I make a response).
     
  10. Nov 2, 2014 #9
    Last edited: Nov 2, 2014
  11. Nov 2, 2014 #10

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    That's too bad. There's an easy elementary (if somewhat tricky) solution using the substitution I suggested before. Maybe you could show your work in setting up the Weierstrass substitution?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Integration by special technique
  1. Integration techniques (Replies: 6)

  2. Integration techniques (Replies: 5)

  3. Integration techniques (Replies: 4)

  4. Integration techniques (Replies: 1)

Loading...