Question

求下题答案~~

设L是由原点O沿抛物线y=x²，到点A(1,1)，再由点A沿直线y=x到原点的封闭曲线，则曲线积分∮L arctan(y/x)dy－dx=

Answer 1

（具体算法是这样的，具体结果你最好再验证一下）

Answer 2

y=x²,0<=x<=1
∮L arctan(y/x)dy－dx=
=∫(0到1)(arctanxdx^2-dx)
=x^2arctanx(0到1)-∫(0到1)x^2/(1+x^2)dx-1
=π/4-1-∫(0到1)(x^2+1-1)/(1+x^2)dx
=π/4-1-∫(0到1)1-1/(1+x^2)dx
=π/4-2+arctanx|(0到1)
=π/4-2+π/4
=π/2-2