double integrals

Question

Suppose F (x,y)=⟨ex,ey⟩ and C is the portion of the ellipse centered at the origin from the point (0,1) to the point (6,0) centered at the origin oriented clockwise. (a) Find a vector parametric equation r (t) for the portion of the ellipse described above for 0≤t≤π/2. r (t)=?

Answer 1

For ellipse, we can use x = a cos(t), y = b sin(t) or x = a sin(t), y = b cos(t). Here a = 6 and b = 1.

Let x = 6 sin(t), y = cos(t), 0 «t«π/2

We choose this option since it starts from (0,1). When t = 0, x = 6 sin(0) = 0, y = cos(0) = 1. As t increases, sin(t) increases and cos(t) decreases. When t = π/2, x = 6, y = 0 and we reach the point (6,0).

Hope this helps.