[積分] Green's theorem

[plowsavior (咕嚕咕咕)]

Using Green's theorem to evaluate the line integral


      2
　∫(y  - 8y)dx + (2xy + 8x)dy
  c


If C is the circle

    2      2
   x   +  y  =1

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作者: BaBi (迅雷不及掩耳盜鈴) 看板: trans_math
標題: Re: [積分] Green's theorem
時間: Thu Feb 20 20:22:07 2014

※ 引述《plowsavior (咕嚕咕咕)》之銘言：
: Using Green's theorem to evaluate the line integral
:       2
: 　∫(y  - 8y)dx + (2xy + 8x)dy
:   c
: If C is the circle
:     2      2
:    x   +  y  =1

        by Green's Theorem

            2
        ∫(y  - 8y)dx + (2xy + 8x)dy
         c

      = ∫∫[ (2y+8) - (2y-8) ] dxdy

      = 16 ∫∫dxdy = 16(pi)

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推 plowsavior:感謝!!