Results 1 to 7 of 7

Math Help - integral problem

  1. #1
    Newbie
    Joined
    Dec 2011
    Posts
    2

    integral problem

    the integral of (X^3sin(6x)/sin(5x)) from -4 to 4

    using the riemann sum as well?

    post the answer if you know it.

    I have been working on this for almost 4 hours now and can not figure it out.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member TheChaz's Avatar
    Joined
    Nov 2010
    From
    Northwest Arkansas
    Posts
    600
    Thanks
    2

    Re: integral problem

    Quote Originally Posted by richman18 View Post
     \int_{-4}^{4} \frac{x^3 \sin (6x)}{\sin (5x)}dx

    using the riemann sum as well?

    post the answer if you know it.

    I have been working on this for almost 4 hours now and can not figure it out.
    Maybe you would care to reply with what work you have done and/or deadends that you have encountered in your four hours of work?

    (edit)...
    Having now looked at the actual integral.
    The integrand is odd, integrated over an interval centered at zero. You might not be expected to find an antiderivative, but rather an analytic argument for why this integral equals...
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,110
    Thanks
    2

    Re: integral problem

    My initial impression is, "This is an eyeball problem. The value of the integral is zero (0), by inspection. The argument is an odd function and the limits are symmetric about the origin."

    A little more thought suggests I should determine that it actually exists. That sin(5x) in the denominator needs some thought. What do you think about it?

    x = 0, \frac{\pi}{5} + \frac{k\cdot\pi}{5}\;for\;k = \pm 1, 2, 3, 4, 5
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,621
    Thanks
    426

    Re: integral problem

    one more observation ... the integrand has a discontinuity at x = 0
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member TheChaz's Avatar
    Joined
    Nov 2010
    From
    Northwest Arkansas
    Posts
    600
    Thanks
    2

    Re: integral problem

    Quote Originally Posted by skeeter View Post
    one more observation ... the integrand has a discontinuity at x = 0
    And at a few other places ...
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Dec 2011
    Posts
    2

    Re: integral problem

    Thanks for the tips. I will post my work that I have done so far in a little bit. Once again thanks for the help.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor chisigma's Avatar
    Joined
    Mar 2009
    From
    near Piacenza (Italy)
    Posts
    2,162
    Thanks
    5

    Re: integral problem

    Quote Originally Posted by skeeter View Post
    one more observation ... the integrand has a discontinuity at x = 0
    In x=0 the function has a removable singularity [You can easily verify that using l'Hopital rule...] and therefore that has no effects on integrability. Unfortunately in [-4,4] there are several [non-removable...] singularities so that, according to the 'standard' definition, the integral doesn't exist. If we use however the definition of 'Cauchy Principal Value Integral'...

    Cauchy Principal Value -- from Wolfram MathWorld

    ... and consider that f(x) is an odd function, the we can say that is...

    \text{P V} \int_{- a}^{a} f(x)\ dx =0



    Marry Christmas from Serbia

    \chi \sigma
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Integral problem involving the definition of the integral
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: May 23rd 2011, 07:06 AM
  2. integral problem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: July 22nd 2010, 01:06 AM
  3. Integral problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 12th 2010, 01:46 PM
  4. Integral Problem
    Posted in the Calculus Forum
    Replies: 6
    Last Post: September 25th 2009, 06:11 AM
  5. Integral Problem
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: February 3rd 2009, 01:21 AM

Search Tags


/mathhelpforum @mathhelpforum