(Steps Shown) Consider the curve C given parametrically by: x(t)=t^2 √3, y(t)=3 t-1/3 t^3, t ∈ [-3,3] Find the area of the shaded region. Find

Question: Consider the curve C given parametrically by:

$x(t)=t^{2} \sqrt{3}, y(t)=3 t-\frac{1}{3} t^{3}, t \in[-3,3]$

Find the area of the shaded region.
Find the arc length of this curve.
If $C$ is rotated about the $x$ -axis, find the volume of the solid of revolution.
If $C$ is rotated about the y-axis, find the volume of the solid of revolution
If $\mathrm{C}$ is rotated about the $x$ -axis, find the surface area of the surface of revolution.
If $C$ is rotated about the $y$ -axis, find the surface area of the surface of revolution.

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(Steps Shown) Consider the curve C given parametrically by: x(t)=t^2 √3, y(t)=3 t-1/3 t^3, t ∈ [-3,3] Find the area of the shaded region. Find

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