Results 1 to 5 of 5

Math Help - Limits of Integration

  1. #1
    Newbie
    Joined
    Dec 2010
    Posts
    18

    Limits of Integration

    Can I get some help, im trying to view the image of this in space

    r is the region in the first quadrant bounded by the line y=x and
    the curve x^4 +x^2y^2=y^2..
    any idea on the limits for my integral, i think it goes from 0-pi/2 and something
    else
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,412
    Thanks
    1328
    I don't think changing to polar coordinates helps. x^2y^2- y^2= y^2(x^- 1)= -x^4 so y^2= \frac{x^4}{1- x^2} and, in the first quadrant, y= \frac{x^2}{\sqrt{1- x^2}}. That intersects y= x when x= 0 and when \frac{x^4}{1- x^2}= x^2 which is equivalent to x^2= 1- x^2.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Dec 2010
    Posts
    18
    (double integral)

    well my integral is
    (1+x^2 +y^2)^-2
    i think polar coordinates is appropriate.
    but i think 0-pie/2 for theta but what is the limits for r dr?
    clearly you have solved for y, but im not visualizing the line y=x and the curve stated above
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,686
    Thanks
    617
    Hello, begin!

    R\text{ is the region in the first quadrant bounded by the line }y=x \text{and the curve } x^4 +x^2y^2\:=\:y^2

    I would convert to polar coordinates . . .


    We have: . x^2(x^2+y^2) \:=\:y^2

    Then: . r^2\cos^2\!\theta \cdot r^2 \:=\:r^2\sin^2\!\theta \quad\Rightarrow\quad r^2 \:=\:\dfrac{\sin^2\!\theta}{\cos^2\!\theta} \quad\Rightarrow\quad r^2 \:=\:\tan^2\theta

    Area Formula: . \displaystyle A \;=\;\tfrac{1}{2}\int^{\beta}_{\alpha} \!r^2\,d\theta


    We have: . r^2 \,=\,\tan^2\!\theta,\;\alpha = 0,\;\beta = \frac{\pi}{4}

    Go for it!

    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Dec 2010
    Posts
    18
    i have theta goes from 0-pie/2 but what abour r dr
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Integration Limits
    Posted in the Calculus Forum
    Replies: 6
    Last Post: March 7th 2010, 04:25 AM
  2. Limits and integration
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: May 23rd 2009, 07:12 AM
  3. How to set limits of integration
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: December 10th 2008, 12:23 AM
  4. Limits of Integration
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 29th 2008, 12:04 PM
  5. Integration between limits
    Posted in the Calculus Forum
    Replies: 6
    Last Post: June 17th 2008, 02:03 PM

Search Tags


/mathhelpforum @mathhelpforum