Results 1 to 3 of 3

Thread: Vector calculus - area

  1. #1
    Newbie
    Joined
    Apr 2011
    Posts
    13

    Vector calculus - area

    Hello. I have no clue how to do this one. I don't know what the region looks like. I've tried squaring etc but with no avail.

    "A plane region is determined by $\displaystyle y \ge 0$, $\displaystyle y \ge -x$ and $\displaystyle x^2+y^2 \le 3\sqrt{x^2+y^2}-3x$.

    (i) sketch this region
    (ii) find its area"

    How would I do this?

    I've tried this for literally 1.5 hrs and I haven't got it

    Thanks
    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 minifhncc View Post
    Hello. I have no clue how to do this one. I don't know what the region looks like. I've tried squaring etc but with no avail.

    "A plane region is determined by $\displaystyle y \ge 0$, $\displaystyle y \ge -x$ and $\displaystyle x^2+y^2 \le 3\sqrt{x^2+y^2}-3x$.

    (i) sketch this region
    (ii) find its area"

    How would I do this?

    I've tried this for literally 1.5 hrs and I haven't got it

    Thanks
    Hopefully you know polar coordinates if you change you will get

    $\displaystyle r^2 \le 3r-3r\cos(\theta) \iff r \le 3(1-\cos(\theta))$

    Now since

    $\displaystyle y \ge 0 \text{ and } y \ge -x$

    This gives that

    $\displaystyle \theta \in [0, \frac{3\pi}{4}]$

    The area can be calculated as follows

    $\displaystyle \int_{0}^{\frac{3\pi}{4}}\int_{0}^{3(1-\cos(\theta))}rdrd\theta$
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2011
    Posts
    13
    OMG THANK YOU THANK YOU!!! I cannot thank you enough!! Thanks again! I'm so stupid arghhh!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Vector Calculus (Position Vector)
    Posted in the Calculus Forum
    Replies: 6
    Last Post: Aug 23rd 2011, 01:43 PM
  2. Vector Calculus (area)
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Jun 21st 2011, 05:26 PM
  3. Vector Calculus (area II)
    Posted in the Calculus Forum
    Replies: 3
    Last Post: Jun 21st 2011, 09:39 AM
  4. vector calculus - vector feilds
    Posted in the Calculus Forum
    Replies: 3
    Last Post: Feb 25th 2010, 01:17 AM
  5. help me with these vector calculus
    Posted in the Calculus Forum
    Replies: 0
    Last Post: Mar 5th 2008, 08:08 PM

Search Tags


/mathhelpforum @mathhelpforum