Results 1 to 5 of 5

Math Help - Integrals

  1. #1
    Junior Member
    Joined
    Nov 2008
    Posts
    34

    Integrals

    Hello! I should determine the values of the following integrals without really calculating:

    (1) \int \limits_{B(2, \pi)}^{} \exp(x) \cdot \cos(y) dx dy

    (2) \int \limits_{\partial B(x_0, \epsilon)}^{} \log(|x|) dS(x), with 0<\epsilon<|x_0|, x_0 \in \mathbb{R}^2.

    I do not have any clue how to solve this exercise. How can one see the values of these integrals?

    Can somebody please help me?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Nov 2008
    Posts
    34
    Does really nobody have an idea? Or a hint? I am completely stuck . I would be thankful for any answers...

    Greetings
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by gammafunction View Post
    Hello! I should determine the values of the following integrals without really calculating:

    (1) \int \limits_{B(2, \pi)}^{} \exp(x) \cdot \cos(y) dx dy

    (2) \int \limits_{\partial B(x_0, \epsilon)}^{} \log(|x|) dS(x), with 0<\epsilon<|x_0|, x_0 \in \mathbb{R}^2.

    I do not have any clue how to solve this exercise. How can one see the values of these integrals?

    Can somebody please help me?
    You could help us by stating what you want B(2, \pi) to denote.

    CB
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by gammafunction View Post
    Does really nobody have an idea? Or a hint? I am completely stuck . I would be thankful for any answers...

    Greetings
    If you have recieved no response you should consider providing more information or clarification for your question.

    Bumping, which is what this post is, is against the rules here and in this case unnecessary you have not recieved an answer because your notation for the volume (and surface) over which the integrals are to be evaluated are not clear. So just provide more explanation in a follow-up post.

    CB
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Nov 2008
    Posts
    34
    Sorry, i did not want to be impatient, i was just interested . And sorry for that mistake, it should of course be the ball around (2,\pi) with radius r, i will change that.

    But i have a solution: as both functions are harmonic (log|x| being the real part of a holomorphic function) one can use the mean-value theorem which gives the following values for the integrals:
    \int \limits_{B((2, \pi),r)}^{} \exp(x) \cdot \cos(y) dx dy=-r^2 \pi \exp(2) and

    \int \limits_{\partial B(x_0, \epsilon)}^{} \log(|x|) dS(x)=2r \pi \log(|x_0|)

    Greetings
    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, 10:23 PM
  2. Replies: 1
    Last Post: December 6th 2009, 08:43 PM
  3. Integrals : 2
    Posted in the Calculus Forum
    Replies: 4
    Last Post: November 24th 2009, 08:40 AM
  4. Integrals and Indefinite Integrals
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 9th 2009, 05:52 PM
  5. integrals Help please
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 8th 2008, 07:16 PM

Search Tags


/mathhelpforum @mathhelpforum