Curve P is defined for by

MATHEMATICS · Subjective · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

Curve P is defined for

0 \le t \le 4

x=2t,\;y=3

. Curve Q is defined on the same interval by

x=2t,\;y=3+\sin t

. Without performing any integrations, determine which curve is longer on

0 \le t \le 4

and state one concise reason for your choice.