Results 1 to 5 of 5

Math Help - Area of the region?

  1. #1
    Newbie
    Joined
    May 2009
    Posts
    5

    Area of the region?

    guuh, I've been working on this problem forever and can't get it.

    Find the area of the region bounded by the graphs f(x) = -x^2 + 7x + 20 and g(x) = x^2 + 5x - 40

    To get the left and right x values

    I do f(x) = g(x)

    x^2 + 7x + 20 = x^2 + 5x - 40

    2x^2 - 2x - 60 = 0

    but then I'm stuck

    ... I think i know what to do once I get the values though
    Last edited by mr fantastic; May 12th 2009 at 04:52 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Calculusretard View Post
    guuh, I've been working on this problem forever and can't get it.

    Find the area of the region bounded by the graphs f(x) = -x^2 + 7x + 20 and g(x) = x^2 + 5x - 40

    To get the left and right x values

    I do f(x) = g(x)

    x^2 + 7x + 20 = x^2 + 5x - 40

    2x^2 - 2x - 60 = 0

    but then I'm stuck

    ... I think i know what to do once I get the values though
    Since you're studying calculus you're expected to be able to solve a quadratic equation. The x-coordinates of the intersection points are x = 6 and x = -5.

    Draw a graph of the two curves and shade the required region. You should know that the enclosed area is given by \int_{-5}^{6} \text{Upper curve} - \text{Lower curve} \, dx.

    It should be crystal clear from your graphs which is the upper curve and which is the lower curve. The integration is routine.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Banned
    Joined
    Feb 2009
    From
    Posts
    79
    2x^{2} -2x -60 =0


      x^{2} -x -30 = 0

    (x-6)(x+5)=0

    x = -5 ,6

    Does that help ?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    May 2009
    Posts
    5
    Ick. I got the wrong answer >_<

    Thank you both for the responses!! Can either of you please tell me what I'm doing wrong/how to do it right!?

    6
    ∫ -x^2 + 7x +20 - (x^2 +5x - 40) dx
    -5

    6
    ∫ -2x^2 + 2x + 60
    -5


    (-2x^3)/ 3 + (2x^2)/ 2

    (-2(6)^3)/ 3 + (2(6)^2)/ 2 - ((-2(-5)^3)/ 3 + (2(-5)^2)/ 2)

    And then I simplified it until I got 865/3 ... which is the wrong answer
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    May 2007
    Posts
    237
    Quote Originally Posted by Calculusretard View Post
    Ick. I got the wrong answer >_<

    Thank you both for the responses!! Can either of you please tell me what I'm doing wrong/how to do it right!?

    6
    ∫ -x^2 + 7x +20 - (x^2 +5x - 40) dx
    -5

    6
    ∫ -2x^2 + 2x + 60
    -5


    (-2x^3)/ 3 + (2x^2)/ 2

    (-2(6)^3)/ 3 + (2(6)^2)/ 2 - ((-2(-5)^3)/ 3 + (2(-5)^2)/ 2)

    And then I simplified it until I got 865/3 ... which is the wrong answer
    The graph of the region.
    Attached Thumbnails Attached Thumbnails Area of the region?-region.gif  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Area of a region
    Posted in the Algebra Forum
    Replies: 2
    Last Post: March 28th 2010, 08:06 AM
  2. Area of region
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 27th 2009, 02:46 AM
  3. Area of Region
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 10th 2009, 12:11 PM
  4. Area of a region
    Posted in the Calculus Forum
    Replies: 5
    Last Post: May 6th 2009, 12:39 PM
  5. Area of a region
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 18th 2006, 10:56 PM

Search Tags


/mathhelpforum @mathhelpforum