The question

For the vector fieldFi- zj+ (y + 1)kcalculate where the path C from (0, 0, -1) to (0, 0, 1) is the circle in the plane x = 0, the direction of motion being anti-clockwise when viewed from the positive x-axis.

My attempt

Let z = sin(t), y = cos(t)

C(t) = (0, cos(t), sin(t))

C'(t) = (0, -sin(t), cos(t))

F(C(t)) =i-j+k

=i- sin(t)j+ (cos(t) + 1)k

(1, -sin(t), cos(t) + 1).(0, -sin(t), cos(t))

= 1 + cos(t)

= 2 + 2sin(1)

However the solution is .

Where have I gone wrong? Thanks.