Results 1 to 3 of 3

Math Help - Find the maximum over a given range?

  1. #1
    Newbie
    Joined
    Apr 2008
    Posts
    15

    Find the maximum over a given range?

    Hello,

    I've been searching through my book and all over to try to find out how to do this, I feel like there is some easy way I'm just forgetting so I'm hoping someone can help me

    Lets say I'm given the following integral:

    \int_0^1 \sin{\frac {\Theta^2}{2}}d\Theta
    (First time using LaTex)

    And I need to find the approximation of the area using Simpson's Rule.
    I can do all that fine but then the problem comes when finding the error.

    I know the error's formula and all but how do I find the value of K, where K is the maximum value the function reaches over a given range [0,1]?

    What methods do we have to find the value of K (over the specified range), especially when it comes to more complicated integrals? My professor never really went over that and I'm just having a tough time getting the questions done.

    Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,621
    Thanks
    426
    Quote Originally Posted by trigoon View Post
    Hello,

    I've been searching through my book and all over to try to find out how to do this, I feel like there is some easy way I'm just forgetting so I'm hoping someone can help me

    Lets say I'm given the following integral:

    \int_0^1 \sin{\frac {\Theta^2}{2}}d\Theta
    (First time using LaTex)

    And I need to find the approximation of the area using Simpson's Rule.
    I can do all that fine but then the problem comes when finding the error.

    I know the error's formula and all but how do I find the value of K, where K is the maximum value the function reaches over a given range [0,1]?

    What methods do we have to find the value of K (over the specified range), especially when it comes to more complicated integrals? My professor never really went over that and I'm just having a tough time getting the questions done.

    Thanks!
    the max possible value for \sin\left(\frac{\theta^2}{2}\right) is 1, and occurs when \frac{\theta^2}{2} = \frac{\pi}{2} , or when \theta = \sqrt{\pi} \approx 1.772 , outside the given interval [0,1].

    since \sin\left(\frac{\theta^2}{2}\right) is strictly increasing on \left[0,\frac{\pi}{2}\right] , then the max value would occur when \theta = 1 on the interval [0,1].
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2008
    Posts
    15
    Ah maybe that wasnt the best example, what about when I have something like this:

    \int_1^2 \frac {\ln(x)}{1+x}dx

    Are there any methods to do these types?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. what is the range (minimum and maximum values of:
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: March 10th 2011, 12:52 PM
  2. Replies: 1
    Last Post: June 25th 2009, 08:01 PM
  3. Find the range
    Posted in the Algebra Forum
    Replies: 2
    Last Post: April 22nd 2009, 06:09 PM
  4. Find the Range
    Posted in the Algebra Forum
    Replies: 4
    Last Post: November 29th 2008, 05:07 AM
  5. Find range of...?
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: September 17th 2008, 05:39 AM

Search Tags


/mathhelpforum @mathhelpforum