ISNS 2367 Lecture 5: Chapter 5 - Study Questions

Match the parametric equations with the correct graph (labeled I-IV).

(a) x = t cos(t), y = t, z = t sin(t),    t ≥ 0

(b) x = cos(t), y = sin(t), z = 1/(1+t²) 

(c) x = t, y = 1/(1+t²) , z = t²

(d) x = cos(t), y = sin(t), z = cos(2t)

Match the parametric equations with the correct graph (labeled I-IV).

(a) x = t cos(t), y = t, z = t sin(t),    t ≥ 0

(b) x = cos(t), y = sin(t), z = 1/(1+t²) 

(c) x = t, y = 1/(1+t²) , z = t²

(d) x = cos(t), y = sin(t), z = cos(2t)

Evaluate the line integral \int_C \mathbf{F}\cdot d\mathbf{r}, where \mathbf{F}(x,y,z) = 4 \sin x \mathbf{i} + 2 \cos y \mathbf{j} + 5x z\mathbf{k} and C is given by the vector function \mathbf{r}(t) = t^3 \mathbf{i} - t^2 \mathbf{j} + t^1 \mathbf{k} , \quad 0 \le t \le 1.