Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Integration continued

  1. Jan 25, 2006 #1
    I have been asked to find the integral sinx cox dx and the integral x sinx cosx dx using the identity sin2x = 2sinxcosx

    I don't know what to do. Can anyone help please, hints,.... answers? :-)
     
  2. jcsd
  3. Jan 25, 2006 #2

    StatusX

    User Avatar
    Homework Helper

    You can integrate sin(2x), right?
     
  4. Jan 25, 2006 #3
    is it -2 cos x?
     
  5. Jan 25, 2006 #4

    StatusX

    User Avatar
    Homework Helper

    Don't guess. You can check to see if the derivative of that gives you back sin(2x). It doesn't, and doing that should help you see what would.
     
  6. Jan 25, 2006 #5

    VietDao29

    User Avatar
    Homework Helper

    As StatusX has pointed out, it's not!
    Looking at your integral table (if integration is new to you, then it's best to have an integral table with you when integrating), you should see something that reads:
    [tex]\int \sin x dx = - \cos x + C[/tex]
    Since x is a dummy variable, x can be anything, such as:
    [tex]\int \sin u du = - \cos u + C[/tex]
    [tex]\int \sin \left( e ^ x \right) d \left( e ^ x \right) = - \cos \left( e ^ x \right) + C[/tex]...
    So you should use a u-substitution here. What is u? (u = ?)
     
    Last edited: Jan 25, 2006
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook