设n边形的n个顶点按逆时针向依次为M<sub>1</sub>(x<sub>1</sub>,y<sub>1</sub>),M<sub>2</sub>(x<sub>2</sub>,y<sub>2</sub>),…,M<sub>n</sub>(x<sub>

设n边形的n个顶点按逆时针向依次为M<sub>1</sub>(x<sub>1</sub>,y<sub>1</sub>),M<sub>2</sub>(x<sub>2</sub>,y<sub>2</sub>),…,M<sub>n</sub>(x<sub>n</sub>,y<sub>n</sub>)。试利用曲线积分证明此n边形的面积为 A=1/2[(x<sub>1</sub>y<sub>2</sub>-x<sub>2</sub>y<sub>1</sub>)+(x<sub>2</sub>y<sub>3</sub>-x<sub>3</sub>y<sub>2</sub>)+...+(x<sub>n-1</sub>y<sub>n</sub>-x<sub>n</sub>y<sub>n-1</sub>)+(x<sub>n</sub>y<sub>1</sub>-x<sub>1</sub>y<sub>n</sub>)]。

时间:2024-04-18 10:52:56

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