Results 1 to 2 of 2

Thread: Area bounded by parametric equations

  1. #1
    Super Member
    Joined
    Dec 2009
    Posts
    755

    Area bounded by parametric equations

    The curve $\displaystyle L$ is defined by the parametric equations

    $\displaystyle x=e^t$ , $\displaystyle y=t-2$

    Find the area of the region enclosed by the curve $\displaystyle L$, the x-axis and the lines $\displaystyle x=e$ and $\displaystyle x=e^3$

    $\displaystyle Area=\int^{e^3}_et-2dx$

    $\displaystyle \frac{dx}{dt}=e^t$

    $\displaystyle Area=\int^{3}_1(t-2)e^tdt$

    $\displaystyle =((3-2)e^3)-((1-2)e)$

    $\displaystyle =e^3+e$

    $\displaystyle =22.8 unit^2$

    But answer is 9.34unit^2
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Jester's Avatar
    Joined
    Dec 2008
    From
    Conway AR
    Posts
    2,470
    Thanks
    83

    Re: Area bounded by parametric equations

    If you draw a picture of the region in question, you'll find that y is negative for t = 1 to 2 then goes positive. You'll need to split your integral up into two pieces to account for that.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. area bounded by parametric equation
    Posted in the Calculus Forum
    Replies: 0
    Last Post: Apr 28th 2010, 03:28 PM
  2. Replies: 2
    Last Post: Mar 10th 2010, 12:40 PM
  3. Replies: 2
    Last Post: Nov 19th 2009, 06:12 AM
  4. Area and Parametric Equations
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Apr 1st 2008, 10:44 PM
  5. Replies: 6
    Last Post: Mar 25th 2008, 08:26 AM

Search Tags


/mathhelpforum @mathhelpforum