A Wire in the Shape of the Curve $x = t ^ { 3 } , y = 2 t ^ { \frac { 3 } { 2 } } , z = 3 t + 1,0 \leq t \leq 1$

question 181

Short Answer

A wire in the shape of the curve $x = t ^ { 3 } , y = 2 t ^ { \frac { 3 } { 2 } } , z = 3 t + 1,0 \leq t \leq 1$ has density function $p ( x , y , z ) = y ^ { 2 } + 1$ . Find the mass of the wire.

---

Definitions:

Garnet

A fairly common silicate mineral with a distinctive shape but nearly any color (red is most common).

Chlorite

Chlorite refers to a group of minerals that often occurs as green flakes in metamorphic rocks and is characterized by its sheet silicate structure.

Thrust Fault

A type of geological fault where one rock stratum is pushed up and over another because of compressional forces, often associated with mountain building.

Propagates Upward

Refers to a process or effect that moves or spreads from a lower point to a higher point in a system or structure.