Results 1 to 8 of 8

Math Help - Finding Average Value

  1. #1
    Junior Member
    Joined
    Nov 2007
    From
    New York City
    Posts
    36

    Finding Average Value

    1) Find the average value of the function over the indicated interval:
    x^2-sin(x) on [-2,4].

    I am not sure how to go about solving this problem. Any help on it will be much appreciated!

    -M
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by blurain View Post
    1) Find the average value of the function over the indicated interval:
    x^2-sin(x) on [-2,4].

    I am not sure how to go about solving this problem. Any help on it will be much appreciated!

    -M
    The average value of a function f(x) on an interval [a,b] is given by:

    \mbox{Average Value } = \frac 1{b - a} \int_a^b f(x)~dx
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Nov 2007
    From
    New York City
    Posts
    36
    Thank you for replying. However, I already know the formula to find the average value; I just do not understand the algebraic part of the problem.

    -M
    Follow Math Help Forum on Facebook and Google+

  4. #4
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by blurain View Post
    Thank you for replying. However, I already know the formula to find the average value; I just do not understand the algebraic part of the problem.

    -M
    by "algebraic" do you mean finding the integral \frac 16 \int_{-2}^4 \left( x^2 - \sin x \right)~dx ?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Nov 2007
    From
    New York City
    Posts
    36
    Ah, yes, that was what I meant.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by blurain View Post
    Ah, yes, that was what I meant.
    in general, \int x^n~dx = \frac {x^{n + 1}}{n + 1} + C for n \ne -1

    if n = -1, \int x^{-1}~dx = \ln x + C

    \int \sin x ~dx = - \cos x + C

    now can you continue?

    you do know how to plug in the limits of integration according to the fundamental theorem of calculus, right?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Junior Member
    Joined
    Nov 2007
    From
    New York City
    Posts
    36
    Would that mean that x^2-sin(x) is 1/3(x^3)+cos(x)?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by blurain View Post
    Would that mean that x^2-sin(x) is 1/3(x^3)+cos(x)?
    yes, that's the integral. now plug in the limits. and don't forget that you have a 1/6 in front
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Finding the average velocity
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 8th 2010, 01:48 AM
  2. Replies: 8
    Last Post: October 23rd 2009, 01:07 PM
  3. Finding the average value of this function
    Posted in the Calculus Forum
    Replies: 5
    Last Post: March 5th 2009, 02:25 PM
  4. Finding Average Speed
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: September 28th 2008, 11:12 AM
  5. finding the average
    Posted in the Algebra Forum
    Replies: 1
    Last Post: July 31st 2005, 09:00 PM

Search Tags


/mathhelpforum @mathhelpforum