Find the Length of the Curve $x = t ^ { 3 } \cos t , y = t ^ { 3 } \sin t , 0 \leq t \leq 3$

question 74

Essay

Find the length of the curve $x = t ^ { 3 } \cos t , y = t ^ { 3 } \sin t , 0 \leq t \leq 3$ using a graphing calculator to evaluate the integral.

---

Definitions:

Dermis

The layer of skin situated beneath the epidermis, containing nerve endings, sweat and sebaceous glands, and blood and lymph vessels.

Papillary Layer

The uppermost layer of the dermis, directly beneath the epidermis, containing loose connective tissue and capillaries, which nourish the epidermis and house touch and pain receptors.

Subcutaneous Layer

A layer of tissue lying immediately under the skin, composed mainly of fat and connective tissues, providing insulation and energy storage.

Adipose Tissue

A type of body tissue containing stored fat that serves as a source of energy, insulates the body, and protects organs.