Results 1 to 7 of 7

Math Help - Equal Areas

  1. #1
    Member McScruffy's Avatar
    Joined
    Jul 2009
    Posts
    87
    Awards
    1

    Equal Areas

    I could use some help with the setup on this one:

    The line y=c intersects the curve y=2x-3x^3 in the first quadrant (see image). Find c such that area a is equal to area b.

    Thanks.
    Attached Thumbnails Attached Thumbnails Equal Areas-problem.gif  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    28
    where a and b are the intersection points of these to functions

    then solve \int_0^a~c-(2x-3x^3)~dx = \int_a^b~2x-3x^3-c~dx

    Not 100% sure where it will lead but I think the logic is something to follow.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member Random Variable's Avatar
    Joined
    May 2009
    Posts
    959
    Thanks
    3
    Quote Originally Posted by pickslides View Post
    where a and b are the intersection points of these to functions

    then solve \int_0^a~c-(2x-3x^3)~dx = \int_a^b~2x-3x^3-c~dx

    Not 100% sure where it will lead but I think the logic is something to follow.
    It seems to lead to  b^{2}-\frac{3}{4}b^{4}-cb =0

    But you also know that 2b-3b^{3}=c


    EDIT: I probably shouldn't be using a and b for limits.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member McScruffy's Avatar
    Joined
    Jul 2009
    Posts
    87
    Awards
    1
    Quote Originally Posted by Random Variable View Post
    It seems to lead to  b^{2}-\frac{3}{4}b^{4}-cb =0

    But you also know that 2b-3b^{3}=c


    EDIT: I probably shouldn't be using a and b for limits.
    Either way, I get the idea.
    Thank you both.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member Random Variable's Avatar
    Joined
    May 2009
    Posts
    959
    Thanks
    3
    I get  a = \frac{\text{-1}}{3} + \frac{\sqrt{3}}{3}, \ b = \frac{2}{3}, \ \text{and} \ c = \frac{12}{27}
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member McScruffy's Avatar
    Joined
    Jul 2009
    Posts
    87
    Awards
    1
    Quote Originally Posted by Random Variable View Post
    I get  a = \frac{\text{-1}}{3} + \frac{\sqrt{3}}{3}, \ b = \frac{2}{3}, \ \text{and} \ c = \frac{12}{27}
    I got the same thing, c=\frac{4}{9}.
    Thanks again.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Super Member Random Variable's Avatar
    Joined
    May 2009
    Posts
    959
    Thanks
    3
    Quote Originally Posted by McScruffy View Post
    I got the same thing, c=\frac{4}{9}.
    Thanks again.
    I need to retake third grade math and relearn how to reduce a fraction.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Equal power sets -> Equal sets?
    Posted in the Discrete Math Forum
    Replies: 6
    Last Post: July 5th 2012, 09:23 AM
  2. Equal Areas of triangles and quadrilateral
    Posted in the Geometry Forum
    Replies: 1
    Last Post: April 8th 2011, 03:12 AM
  3. Replies: 5
    Last Post: February 24th 2011, 04:08 PM
  4. sum of areas
    Posted in the Algebra Forum
    Replies: 3
    Last Post: November 22nd 2009, 07:16 PM
  5. Replies: 2
    Last Post: March 23rd 2009, 07:11 AM

Search Tags


/mathhelpforum @mathhelpforum