題目
Problem
PART 1: Fill in the blanks.
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Work need not be shown, only answers will be graded.
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4 points for each blank and 100 points total.
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Each answer need to be clearly labeled on the answer sheet.
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Use of any device with computer algebra system during the exam will result in zero points.
- Let C be the curve consisting of line segments from (0,0) to (2,1) to (1,2) to (0,0).
∫C(x−y)dx+(2x+y)dy=(24).
解答
解法一
思路
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封閉折線圍成的區域簡單,適合用格林定理把線積分化成面積積分。
答題過程
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路徑為逆時針三角形,面積為 3/2。令 P=x−y,Q=2x+y,格林定理給出
∮CPdx+Qdy=∬R(∂x∂Q−∂y∂P)dA=∬R3dA=29.