Results 1 to 3 of 3

Math Help - Area of a Plane region helppp

  1. #1
    Senior Member
    Joined
    Jul 2006
    From
    Shabu City
    Posts
    381

    Area of a Plane region helppp

    i cant hit the answer key;
    (this is an application of Integration)
    Find the area of the region bounded by the two curves
    y = x^3 + 3x^2 + 2x; y = 2x^2 + 4x

    answer: 37/12 sq units
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123
    Quote Originally Posted by ^_^Engineer_Adam^_^ View Post
    i cant hit the answer key;
    (this is an application of Integration)
    Find the area of the region bounded by the two curves
    y = x^3 + 3x^2 + 2x; y = 2x^2 + 4x

    answer: 37/12 sq units
    Hello,

    I've attached an image of the grapghs and the enclosed area.

    First calculate the intersections of the 2 graphs:

    x + 3x + 2x = 2x + 4x ===> x + x - 2x = 0 The LHS can be factorized:

    x + x - 2x = x(x + 2)(x - 1)

    To calculate the enclosed area you use the difference of the 2 functions:

    d(x) = x + x - 2x

    A = |∫[from -2 to 0](x + x - 2x)dx| + |∫[from 0 to 1](x + x - 2x)dx|

    A = |[from -2 to 0]( x^4 + (1/3)x - x)dx| + |[from 0 to 1]( x^4 + (1/3)x - x)dx|

    A = |0 - (-8/3)| + |(-5/12) - 0| = 37/12

    EB
    Attached Thumbnails Attached Thumbnails Area of a Plane region helppp-eingeschl_flaeche2.gif  
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    13
    Quote Originally Posted by earboth View Post
    x + x - 2x = x(x + 2)(x - 1)
    Define f(x) = x + 3x + 2x and g(x) = 2x + 4x

    In [0,1] --> f(x) < g(x); in [-2,0] --> g(x) < f(x), then the definite integral to find is



    Last edited by Krizalid; March 31st 2007 at 09:09 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. determine a region in the xy plane...
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: January 25th 2011, 11:02 PM
  2. Z-plane region
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 28th 2009, 10:45 PM
  3. Area of region of plane between the graph
    Posted in the Calculus Forum
    Replies: 6
    Last Post: April 14th 2009, 09:21 AM
  4. Replies: 5
    Last Post: April 15th 2008, 02:33 AM
  5. Area of a plane region
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 30th 2007, 11:26 AM

Search Tags


/mathhelpforum @mathhelpforum