Results 1 to 2 of 2

Thread: Area between Curves

  1. #1
    Super Member
    Joined
    Jun 2009
    From
    United States
    Posts
    680
    Thanks
    19

    Area between Curves

    I want to find the area between the curves $\displaystyle y=12-x^2$ and $\displaystyle y=x^2-6$. If you graph these functions, you can see they intersect at $\displaystyle (-3,3)$ and $\displaystyle (3,3)$. The graph is also symmetric about the y-axis, so I will find the area by finding the area of the left side, and mulitplying it by two. I will chop the left hand side, into two areas $\displaystyle A_1$ and $\displaystyle A_2$ where $\displaystyle A_1=\int_{3}^{12}\sqrt{12-y}dy$ and $\displaystyle A_2=\int_{-6}^{3}\sqrt{y+6}dy$. The total area will be:

    $\displaystyle A=2(A_1+A_2)$

    $\displaystyle =2\left(\int_{3}^{12}\sqrt{12-y}dy+\int_{-6}^{3}\sqrt{y+6}dy\right)$

    Am I setting this up right?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    16,216
    Thanks
    3702
    Quote Originally Posted by adkinsjr View Post
    I want to find the area between the curves $\displaystyle y=12-x^2$ and $\displaystyle y=x^2-6$. If you graph these functions, you can see they intersect at $\displaystyle (-3,3)$ and $\displaystyle (3,3)$. The graph is also symmetric about the y-axis, so I will find the area by finding the area of the left side, and mulitplying it by two. I will chop the left hand side, into two areas $\displaystyle A_1$ and $\displaystyle A_2$ where $\displaystyle A_1=\int_{3}^{12}\sqrt{12-y}dy$ and $\displaystyle A_2=\int_{-6}^{3}\sqrt{y+6}dy$. The total area will be:

    $\displaystyle A=2(A_1+A_2)$

    $\displaystyle =2\left(\int_{3}^{12}\sqrt{12-y}dy+\int_{-6}^{3}\sqrt{y+6}dy\right)$

    Am I setting this up right?

    finding the area w/r to x is much easier ...

    $\displaystyle A = 2 \int_0^3 (12-x^2) - (x^2-6) \, dx$
    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: Mar 15th 2011, 03:24 PM
  2. Area between two curves
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Aug 11th 2010, 09:52 PM
  3. area between curves.
    Posted in the Calculus Forum
    Replies: 6
    Last Post: Jan 11th 2010, 11:39 AM
  4. Area Between Two Curves
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Mar 10th 2009, 03:15 PM
  5. Area Between Curves
    Posted in the Calculus Forum
    Replies: 5
    Last Post: Dec 17th 2008, 02:06 PM

Search Tags


/mathhelpforum @mathhelpforum