题目
设 L: y = 1 - x, (a leq x leq b)，则下列曲线积分转化为定积分正确表达式是(）。A. int_(L) f(x, y), ds = int_(b)^a f(x, 1 - x)sqrt(2) , dxB. int_(L) f(x, y), ds = int_(1-b)^1-a f(1 - y, y)sqrt(2) , dyC. int_(L) f(x, y), ds = int_(1-a)^1-b f(1 - y, y)sqrt(2) , dyD. int_(L) f(x, y), ds = int_(1-b)^1-a f(1 - y, y), dy
设 $L: y = 1 - x, (a \leq x \leq b)$，则下列曲线积分转化为定积分正确表达式是(）。
A. $\int_{L} f(x, y)\, ds = \int_{b}^{a} f(x, 1 - x)\sqrt{2} \, dx$
B. $\int_{L} f(x, y)\, ds = \int_{1-b}^{1-a} f(1 - y, y)\sqrt{2} \, dy$
C. $\int_{L} f(x, y)\, ds = \int_{1-a}^{1-b} f(1 - y, y)\sqrt{2} \, dy$
D. $\int_{L} f(x, y)\, ds = \int_{1-b}^{1-a} f(1 - y, y)\, dy$
题目解答
答案
C. $\int_{L} f(x, y)\, ds = \int_{1-a}^{1-b} f(1 - y, y)\sqrt{2} \, dy$