The discussion focuses on calculating the work done by the force field \( F(x,y) = (ye^{xy})i + (1 + xe^{xy})j \) along the curve \( \gamma(t) = (2t-1, t^2-t) \) for \( t \) in the interval [0,1]. The work is expressed as the line integral \( \int_\gamma \mathbf F(\mathbf s) \cdot d\mathbf s = \int_0^1 \mathbf F(\boldsymbol\gamma(t)) \cdot \boldsymbol\gamma'(t) \, dt \). The discussion also raises the question of whether the force field is conservative and if a potential energy function \( V(x,y) \) exists such that \( \mathbf F(x,y) = \frac{\partial V}{\partial x} \mathbf{i} + \frac{\partial V}{\partial y} \mathbf{j} \).
PREREQUISITESStudents and professionals in mathematics, physics, and engineering who are working with multivariable calculus, particularly in applications involving line integrals and force fields.
kenporock said:calculate the work done by the force field $F(x,y)=(ye^{xy})i+(1+xe^{xy})j$ by moving a particle along the curve C described by
gamma (γ):[0,1] in $R^2$, where gamma (γ)=(2t-1, t²-t)