Results 1 to 4 of 4

Math Help - Please help Area Between curves

  1. #1
    Junior Member
    Joined
    Jan 2008
    Posts
    48

    Please help Area Between curves

    Find the area between the curves:
    y=x^3-12x^2+20x and
    y=-x^3+12x^2-20x
    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 waite3 View Post
    Find the area between the curves:
    y=x^3-12x^2+20x and
    y=-x^3+12x^2-20x
    first, find where the curves intersect. by setting them equal to each other and solving for x. let's say they intersect for x = a and x = b, where a<b. then these are your limits of integration.

    now we need to check which graph is above which. you can simply plug in a value between a and b and see which function gives the higher value. (it is an extremely good idea to graph the curves. just in case they enclose more than one area. you can use a graphing utility to do this)

    Now, let the area between the curves be A.

    we have A = \int_a^b (\mbox{Top function } - \mbox{ Bottom function})~dx

    can you continue?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jan 2008
    Posts
    48
    i keep getting either 0 or 940 but the answer is not correct. any help would be appreciated.
    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 waite3 View Post
    i keep getting either 0 or 940 but the answer is not correct. any help would be appreciated.
    Let f(x) = x^3 - 12x^2 + 20x

    Let g(x) = -x^3 + 12x^2 - 20x

    set f(x) = g(x) \implies f(x) - g(x) = 0

    the solutions are x = 0, ~x = 2, \mbox{ and }x = 10

    with the aid of a graph, we see that the curves enclose areas between [0,2] and [2,10]

    by plugging in x = 1 and x = 3, respectively. we see that:

    for [0,2], f(x) > g(x), and,
    for [2,10], g(x) > f(x).

    Thus, the area is given by:

    A = \int_0^2 [f(x) - g(x)]~dx + \int_2^{10}[g(x) - f(x)]~dx

    now continue
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Area between Curves
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 15th 2011, 03:24 PM
  2. Area between two curves
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 11th 2010, 09:52 PM
  3. area between curves.
    Posted in the Calculus Forum
    Replies: 6
    Last Post: January 11th 2010, 11:39 AM
  4. Area Between Two Curves
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 10th 2009, 03:15 PM
  5. Area between two curves
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 27th 2009, 04:59 PM

Search Tags


/mathhelpforum @mathhelpforum