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Math Help - Vector calculus - area

  1. #1
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    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 y \ge 0, y \ge -x and 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
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  2. #2
    Behold, the power of SARDINES!
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    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 y \ge 0, y \ge -x and 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

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

    Now since

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

    This gives that

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

    The area can be calculated as follows

    \int_{0}^{\frac{3\pi}{4}}\int_{0}^{3(1-\cos(\theta))}rdrd\theta
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  3. #3
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    OMG THANK YOU THANK YOU!!! I cannot thank you enough!! Thanks again! I'm so stupid arghhh!
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