Results 1 to 2 of 2

Math Help - Calculus area

  1. #1
    Junior Member
    Joined
    Oct 2006
    Posts
    36

    Calculus area

    Consider f(x) = x^3 + x^2 + 1 and g(x) = -x^2 + 3x +1
    a) Write the integral to compute the area of the region bounded by f and g.

    I think you would subtract the bottom function from the top function, but what would the integral of integration be?
    Thanks for any help.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member AlvinCY's Avatar
    Joined
    Feb 2007
    From
    I live in Sydney, Australia.
    Posts
    69
    First of all you need to solve for where the two curves intersect.

    Solve simultaneously:

    f(x) = x^3 + x^2 + 1 and g(x) = -x^2 + 3x +1

    x^3 + 2x^2 - 3x = 0

    x (x^2 + 2x - 3) = 0

    x (x + 3)(x - 1) = 0

    so the two curves actually intersect at 3 spots... at

    x = -3, y = -17
    x = 0, y = 1
    and x = 1, y = 3

    Between -3 and 0, we see that f(x) > g(x) and between 0 and 1, we see that g(x) > f(x)

    Therefore, the the area bounded by the two curves should be given by the formula:

    integral from -3 to 0 of [f(x) - g(x)] + integral from 0 to 1 of [g(x) - f(x)]

    :-)

    Hope that helps... and sorry about the notation... the math tags don't seem to be working...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Vector Calculus (area II)
    Posted in the Calculus Forum
    Replies: 3
    Last Post: June 21st 2011, 09:39 AM
  2. Min area using calculus
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 18th 2011, 08:22 AM
  3. Calculus area problem
    Posted in the Calculus Forum
    Replies: 4
    Last Post: March 15th 2010, 08:44 PM
  4. Calculus - maximizing area
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 19th 2009, 03:05 AM
  5. Calculus problem max/area
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 5th 2009, 05:52 PM

Search Tags


/mathhelpforum @mathhelpforum