Results 1 to 2 of 2

Math Help - Integration problem

  1. #1
    Member
    Joined
    Sep 2007
    Posts
    198

    Integration problem

    The curve with equation a^2 y^2 = x^2 (a^2 - x^2) has two loops.
    Show, by integration, that the area enclosed by a loop is \frac {2}{3} a^2.

    Please help me to do this.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by geton View Post
    The curve with equation a^2 y^2 = x^2 (a^2 - x^2) has two loops.
    Show, by integration, that the area enclosed by a loop is \frac {2}{3} a^2.

    Please help me to do this.
    solving the above equation for y we get

    y=\frac{x\sqrt{a^2-x^2}}{a}

    \int_0^{a}\frac{x\sqrt{a^2-x^2}}{a}dx

    is half of the area of one loop. (Draw a graph to see)

    2\int_0^{a}\frac{x\sqrt{a^2-x^2}}{a}dx=

    is the area of one loop. just let u=a^2-x^2

    good luck.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Integration problem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 4th 2010, 09:35 PM
  2. Integration Problem
    Posted in the Calculus Forum
    Replies: 6
    Last Post: March 16th 2010, 04:20 PM
  3. Replies: 2
    Last Post: February 19th 2010, 10:55 AM
  4. Integration problem?
    Posted in the Calculus Forum
    Replies: 6
    Last Post: June 3rd 2009, 06:33 PM
  5. Integration problem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: June 2nd 2008, 02:19 AM

Search Tags


/mathhelpforum @mathhelpforum