## anonymous 4 years ago Consider an object describing an elliptical path in the plane given by r (t) = (2 cos t, 6sin t), where t is in the interval [0, 2]. if the object is subjected to a field with a force given by the expression G (x, y) = (4xy, y^2), calculate the work done by G to move the object along the trajectory from (2, 0) to (0, 6), in direct order.

1. anonymous

$W = \int\limits Gdr$

2. anonymous

just not sure which expression will make easyer to calculate the dot product, paramtric or cartesian.

3. anonymous

probably parametric

4. anonymous

I tried parametric, though it would be easier.

5. anonymous

Use Polar Coordinate x(t)= 2 cos(t) y(t)= 6 sin(t) P = 4 x y Q = y^2 Compute P(x(t),y(t)) x'(t) + Q(x(t),y(t))x'(t)=120 cos(t) sin^2(t) Integrate the last expression for t= to Pi/2 to obtain 40

6. anonymous

This Q(x(t),y(t))x'(t) should be Q(x(t),y(t))y'(t)