Results 1 to 2 of 2

Thread: Integration of a piece wise function?

  1. #1
    Member
    Joined
    Nov 2008
    Posts
    76

    Integration of a piece wise function?

    Determine the value of:

    a) g(-4)
    b) g(-2)
    c) g(1)
    d) g(4)

    The absolute maximum of g(x) occurs when x=....?

    The absolute maximum of g(x) is...?
    Attached Thumbnails Attached Thumbnails Integration of a piece wise function?-calc.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    o_O
    o_O is offline
    Primero Espada
    o_O's Avatar
    Joined
    Mar 2008
    From
    Canada
    Posts
    1,410
    Thanks
    1
    Drawing $\displaystyle f(x)$ out would help. You will see that your graph basically consists of line segments.

    Recall that an integral represents the net area under the curve (from the curve to the x-axis). So all you're doing is calculating the areas of the rectangles (taking into account of the signs).

    For example, to find $\displaystyle g(1) = \int_{-3}^{1} f(t) \ dt$, we want to find the area under the curve from $\displaystyle x = -3$ to $\displaystyle x = 1$

    Since it's a piecewise function, we're going to have to break the integral up into two: $\displaystyle g(1) = \int_{-3}^{1} f(t) \ dt = \int_{-3}^{0} f(t) \ dt + \int_0^1 f(t) \ dt$

    If you look at your graph, the two integrals corresponds to the area under each rectangle that is created. I assume you know how to find the area of a rectangle so hopefully you'll be good from here.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Expressing A Piece Wise Function
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: Oct 15th 2011, 02:00 PM
  2. Integration of piece-wise constant function
    Posted in the Calculus Forum
    Replies: 4
    Last Post: Jun 27th 2011, 12:52 AM
  3. continous piece wise function
    Posted in the Calculus Forum
    Replies: 3
    Last Post: Apr 30th 2010, 08:42 AM
  4. piece wise defined function
    Posted in the Algebra Forum
    Replies: 3
    Last Post: Apr 24th 2010, 09:05 AM
  5. Absolute Value into Piece-Wise Function
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: Sep 30th 2009, 10:35 AM

Search Tags


/mathhelpforum @mathhelpforum