Answer to Question #281347 in Calculus for saisha

Question

Evaluate I = Z C x^ 2 ydx + (x-2y)dy over the part of parabola y=x^2 from (0,0) to (1,1) 

Answer 1

$x(t)=t,y(t)=t^2,0\le t \le 1$

$I=\int^1_0[t^4\frac{dx}{dt}+(t-2t^2)\frac{dy}{dt}] dt=\int^1_0[t^4+2t (t-2t^2)]dt=$

$=(t^5/5+2t^3/3-t^4)|^1_0=1/5+2/3-1=-2/15$