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Math Help - Green's!! Help!

  1. #1
    s7b
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    Green's!! Help!

    Can someone please help;

    I keep getting a really ugly answer I'm sure is wrong

    Use Green's Theorem area formula to find the ares of the region: the ellipse
    r(t)= (acost)i + (bsint)j t between 0 and 2pi
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by s7b View Post
    Can someone please help;

    I keep getting a really ugly answer I'm sure is wrong

    Use Green's Theorem area formula to find the ares of the region: the ellipse
    r(t)= (acost)i + (bsint)j t between 0 and 2pi

    The area formula has a few different (equivelent) ways to be written so here is one

    A=\oint_{C}xdy=-\oint_Cydx

    We can use either one so with the first one we get

    A=\int_{0}^{2\pi}a\cos(t)(b\cos(t)dt=ab\int_{0}^{2  \pi}\cos^{2}(t)dt=\frac{ab}{2}\int_{0}^{2\pi}(1-\cos(2t))dt=
    \frac{ab}{2} \cdot [t-\frac{1}{2}\sin(2t)]\bigg|^{2\pi}_{0}=\pi ab
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  3. #3
    s7b
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    ok, I just figured it out and yeah i got that same answer. Thanks though
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