Question

Suppose \vec{F}(x,y) = -y \sin(x) \vec{i} + \cos(x) \vec{j}.

(a) Find a vector parametric equation for the parabola y = x^2 from the origin to the point \left(3,9\right) using t as a parameter.
\vec{r}(t) =

(b) Find the line integral of \vec{F} along the parabola y = x^2 from the origin to \left(3,9\right).

Answer 1

Suppose vec{F}(x,y) = -y sin(x){i} + cos(x) {j}.

(a) Find a vector parametric equation for the parabola y = x^2 from the origin to the point (3,9) using t as a parameter.
r(t)=?

(b) Find the line integral of vec{F} along the parabola y = x^2 from the origin to (3,9).