# Work done by a force field line integrals

Find the work done by the force field $F(x, y) = \langle 2x \sin(y), 2y \rangle$ on a particle that moves along the parabola $y = x^2$ from $(-1, 1)$ to $(2, 4)$.

So to use line integrals to solve this I took $r(x) = \langle x, x^2 \rangle$. Then $$\int_{-1}^2 \langle 2x \sin{x^2}, 2x^2 \rangle \cdot \langle 1, 2x \rangle = \int_{-1}^2 2x \sin{x^2} + 4x^2 dx.$$ Does that work?

• That looks fine, except the integrand should have $4x^3$, and not $4x^2$ I believe. – msteve Jul 27 '14 at 22:36
• @msteve oh yeah, thanks! – Shaurya Dhingra Jul 27 '14 at 22:37
• @msteve You should make that an answer. – Mark Fantini Jul 27 '14 at 23:34