∫L(-x2-y)dx+(x+y)2dy,其中O(0,0)A(0,1)B(1,1)的折线段

Question

∫L(-x2-y)dx+(x+y)2dy,其中O(0,0)A(0,1)B(1,1)的折线段

Answer 1

线段OA方程：x=0,y：0→1
线段AB方程：y=1,x：0→1
∫L(-x2-y)dx+(x+y)2dy
=∫OA (-x²-y)dx+(x+y)²dy+∫AB (-x²-y)dx+(x+y)²dy
=∫[0→1] y²dy + ∫[0→1] (-x²-1)dx
=(1/3)y³ |[0→1] + [-(1/3)x³-x] |[0→1]
=(1/3)-(1/3)-1
=-1