设L是X^2+Y^2=1的下半圆周,则曲线积分ds的值为多少,求详解

2025-05-05 19:03:22
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回答1:

下半圆周,则y ≤ 0
先化为参数方程:
令x = cost,y = sint,π ≤ t ≤ 2π
则dx = - sint dt,dy = cost dt
则ds = √((dx)² + (dy)²) dt
ds = √(sin²t + cos²t) dt
ds = dt