Question

Determine the work done by a force F =xyi^+yzj^+xzk^ in taking particle along the path defined by the equation r(t)=ti^+2t^2j^+t^3k^,0<_t<_1from t=0 to t=2 is the force conservative

Answer 1

$$W=\int ^1_0(t(2t^2),t^3(2t^2),t(t^2))d(t,2t^2,t^3)\\W=\int ^1_0(2t^3+2t^5(4t)+t^3(3t^2))dt \\W=\int ^1_0(2t^3+8t^6+3t^5)dt=\frac{15}{7}$$

Yes, this force is conservative force.