Set Up an Integral That Represents the Length of the Curve

question 21

Short Answer

Set up an integral that represents the length of the curve. Then use your calculator to find the length correct to four decimal places. $x = t - 2 \sin t , \quad y = 1 - 2 \cos t , \quad 0 \leq t \leq 5 \pi$

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Definitions:

Bad Food Habits

Unhealthy eating patterns or practices that can lead to nutrition-related problems or conditions.

Cognitive-behavioral Interventions

Therapeutic techniques that aim to change patterns of thinking or behavior that are behind people's difficulties, and so change the way they feel.

Physical Activity

Any bodily movement produced by skeletal muscles that require energy expenditure, contributing to physical fitness and overall health.

Negative Affectivity

A personality characteristic involving the predisposition to experience negative emotions such as anger, anxiety, or depression more frequently or intensely than average.