Find the Distance Traveled by a Particle with Position $( x , y ) = \left( \cos ^ { 2 } t , \cos t \right)$

question 112

Essay

Find the distance traveled by a particle with position $( x , y ) = \left( \cos ^ { 2 } t , \cos t \right)$ as t varies in the time interval $[ 0,4 \pi ]$ . Compare with the length of the curve.

---

Definitions:

Indifference Curve

A graphical representation showing different bundles of goods between which a consumer is indifferent, reflecting their preferences and utility.

Total Utility

The overall satisfaction or benefit a consumer receives from consuming a particular quantity of a good or service.

Indifference Curve

A graphical representation showing combinations of goods or services among which a consumer is indifferent, meaning they have no preference for one combination over another, holding utility constant.

Absolute Value

The non-negative value of a number without regard to its sign.