Results 1 to 3 of 3

Math Help - area by multiple integrals

  1. #1
    Senior Member
    Joined
    Feb 2010
    Posts
    456
    Thanks
    34

    area by multiple integrals

    i have two parabolas x=y^2-1 and x=2y^2-2

    i have to find the area between them using multiple integrals

    i know by simple integrals but how to do it by multiple integrals

    please help
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,804
    Thanks
    1576

    Re: area by multiple integrals

    Start by drawing a sketch. You'll see that the region is easiest evaluated using horizontal strips, with each strip bounded on the left by \displaystyle \begin{align*} x = 2y^2 - 2  \end{align*} and on the right bounded by \displaystyle \begin{align*} x = y^2 - 1 \end{align*}. Then when summing all these strips, the strips are bounded below by \displaystyle \begin{align*} y = -1 \end{align*} and bounded above by \displaystyle \begin{align*} y = 1 \end{align*}.

    So the area is given by \displaystyle \begin{align*} \int_{-1}^1{\int_{2y^2 - 2}^{y^2 - 1}{1\,dx}\,dy} \end{align*}.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Oct 2012
    From
    India
    Posts
    61
    Thanks
    3

    Re: area by multiple integrals

    Another approach is to use the difference of these two functions, and integrate that. You have to use modulus (absolute value) of the difference, and divide integration interval depending on the sign of it. In that method, integration limits will be constants, not y^2 -1 and 2y^2 - 2.

    Salahuddin
    Maths online
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. multiple integrals
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 14th 2009, 04:53 PM
  2. Multiple integrals help
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 28th 2009, 01:21 PM
  3. Multiple integrals
    Posted in the Calculus Forum
    Replies: 5
    Last Post: May 26th 2009, 12:53 AM
  4. Multiple Integrals
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 19th 2008, 01:17 PM
  5. Help on multiple integrals?
    Posted in the Advanced Applied Math Forum
    Replies: 1
    Last Post: September 9th 2008, 03:37 AM

Search Tags


/mathhelpforum @mathhelpforum