Problem : Find the length of the parametric curve given by
,(2t + 1)^{3/2} |
dt | = | dt | |
= t + 1dt | |||
= + x | = 4 |
Problem : Compute the length of (t + sin(t), 2 - cos(t)) from t = 0 to 3Π . You may use the trigonometric identity 1 + cos(θ) = 2 cos^{2}(θ/2).
The velocity vector of this parametric curve at time t equals (1 + cos(t), sin(t)) , so the length of the curve is
dt | = | ||
= | dt | ||
= | 2 cos dt | ||
= | 2cos dt + 2 - cos dt | ||
= | 22 sin +2 -2 sin | ||
= | 12. |