# Find the volume using cylindrical shells? (Enclosed by x-axis and parabola #y=3x-x^2#, revolved about #x=-1#)

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So far, I have the bounds at 0 and 3.

...I think I've forgotten how to apply shells, exactly.

Assuming thickness is #dx# , and height is the area given (#3x-x^2# )... then what is the radius? I don't know what that would be (is it #x# ?)

What I have, plugged into equation:

#V=2\pi\int_0^3[r*(3-x^2)dx]#

So far, I have the bounds at 0 and 3.

...I think I've forgotten how to apply shells, exactly.

Assuming thickness is

What I have, plugged into equation:

##### 1 Answer

#### Explanation:

In cylindrical shell method the slice should be parallel to the axis of revolution.

In your question the area bounded revolving around

where

show below the region (shaded) revolving around