A path in the plane is traced in two parts

MATHEMATICS · Subjective · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

A path in the plane is traced in two parts. Segment 1

(0 \le t \le 2): \; x=t, \; y=\dfrac{t^{2}}{2}

Segment 2

(2 \le t \le 4): \; x = 2, \; y = t

Determine the exact total length of the path from

t = 0

t = 4