Results 1 to 15 of 15

Math Help - help proceeding further with a couple integrals

  1. #1
    Newbie
    Joined
    Mar 2011
    Posts
    23

    help proceeding further with a couple integrals

    So I need help integrating this: sqrt(1+cosx)dx

    And integrating :cosxsinxdx on the interval 0 to 2pi.

    Witht the second one I can only get to solutions that result in zero because the final always equals the initial.

    Ideas?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Mar 2011
    Posts
    23
    I figured out the first one, I only need help with the second. Thanks
    Follow Math Help Forum on Facebook and Google+

  3. #3
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    5
    Awards
    2
    For the first problem, what ideas have you had so far?

    For the second problem, have you considered that you might be getting the right answer?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Mar 2011
    Posts
    23
    I used half angle identities and it worked with the first one. Is there an explanation as to why half angle identities work better sometimes?

    For the second one I'm entirely sure its not zero. It goes from ds=3asinxcosxdx and the answer is 6a so somehow integrating sinxcosxdx should be 2.

    Hmmm
    Follow Math Help Forum on Facebook and Google+

  5. #5
    -1
    e^(i*pi)'s Avatar
    Joined
    Feb 2009
    From
    West Midlands, England
    Posts
    3,053
    Thanks
    1
    Consider using a double angle identity
    Follow Math Help Forum on Facebook and Google+

  6. #6
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    5
    Awards
    2
    For the first problem, I would let u=1+\cos(x), and go from there.

    For the second problem, what do you get for the antiderivative?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Mar 2011
    Posts
    23
    I have already with no luck
    ds=3asinxcosxdx=(3a/2)sin(2x)dx from 0 to 2pi. Integrating that you ed up getting zero since the final is equal to the initial.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    5
    Awards
    2
    So, what is that telling you?
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie
    Joined
    Mar 2011
    Posts
    23
    It's not continuous? Not entirely sure what I should be doing from this point. It doesn't give me any help in my textbook that I can note. I have the answer its 6a however I cannot seem to avoid getting zero, no matter how I tackle it.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    5
    Awards
    2
    Quote Originally Posted by profound View Post
    It's not continuous? Not entirely sure what I should be doing from this point. It doesn't give me any help in my textbook that I can note. I have the answer its 6a however I cannot seem to avoid getting zero, no matter how I tackle it.
    What is a? You don't mention a in your original problem statement anywhere. Are you sure you're comparing the right answer to the right problem? I would definitely claim that

    \displaystyle\int_{0}^{2\pi}\sin(x)\cos(x)\,dx=0.
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Just to add my 2 cents with definite integrals use a little geometery to see if you answer is reasonable.

    Notice that \displaystyle \sin(x)\cos(x)=\frac{1}{2}\sin(2x)

    This is a sine function with a peroid of Pi. Whenever you integrate since or cosine over one complete peroid you will get zero. Graph it.

    So if you integrate over two peroids you will still get zero.
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Newbie
    Joined
    Mar 2011
    Posts
    23
    The full question is "ds=3asinxcosxdx" where 3 and a are constants. I left then out because they have no affect on the answer. Anyways, I thought it was zero the whole time but the back of the book said 6a is the answer. Thanks!
    Follow Math Help Forum on Facebook and Google+

  13. #13
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    5
    Awards
    2
    Books have been known to be wrong in their answers before. I'd say the book's answer is wrong - that is, if you're sure that 6a is exactly what the book claims the answer is.
    Follow Math Help Forum on Facebook and Google+

  14. #14
    Newbie
    Joined
    Mar 2011
    Posts
    23
    Haha, just thought I'd check. I strongly dislike when there is a wrong answer, especially when you are learning a new conept!
    Follow Math Help Forum on Facebook and Google+

  15. #15
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    5
    Awards
    2
    Quote Originally Posted by profound View Post
    Haha, just thought I'd check. I strongly dislike when there is a wrong answer, especially when you are learning a new concept!
    I can understand that, but you'd better get used to it: lots of books have lots of typos.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. a couple more definite integrals
    Posted in the Math Challenge Problems Forum
    Replies: 2
    Last Post: March 31st 2011, 09:44 AM
  2. a couple of trigonometric integrals
    Posted in the Calculus Forum
    Replies: 7
    Last Post: December 27th 2010, 08:43 AM
  3. Need help with couple of integrals!
    Posted in the Calculus Forum
    Replies: 9
    Last Post: June 1st 2010, 11:32 AM
  4. a couple integrals
    Posted in the Calculus Forum
    Replies: 4
    Last Post: April 18th 2008, 01:20 PM
  5. A couple of indefinite integrals
    Posted in the Calculus Forum
    Replies: 5
    Last Post: September 18th 2006, 01:29 AM

Search Tags


/mathhelpforum @mathhelpforum