line integral

〈Q１〉　for a line segment C:y=2x (x∊[-1,1]),

calculate int(C) (y＾2-x＾2)ds.

for points of (x,y) on the line C、(x,y)=(x,2x).

ds = root((dx)^2+(dy)^2) = root(5)|dx|=root(5) dx (since x>0)

thefore, 

int_0^1 (3root(5)x^2)dx = root(5)■

〈Q2〉　calculate int(C) (x+y)ds.

where C={(x,y)|x^2+y^2=1, y>=0, x∊[-1,1] }

x = -cosθ, y = sinθ (θ：0->pi) 

ds = root((dx)^2+(dy)^2) = |dθ|=dθ (since θ>0)

therefore, 

int_0^(pi) (-cosθ, y = sinθ) dθ = 2■