Use the shell method to write and evaluate the definite integral that represents the volume of the solid generated by revolving the plane region about the y-axis. y

The volume of the solid of revolution generated by revolving the plane region about the y-axis is cubic units.

Let be and , whose point of intersection is . Solid of revolution generated by revolving the plane region about the y-axis is defined by the following formula:

(1)

If we know that , then the volume of the solid of revolution is:

The volume of the solid of revolution generated by revolving the plane region about the y-axis is cubic units.

The statement is incomplete. Complete form is shown below:

Use the shell method to write and evaluate the definite integral that represents the volume of the solid generated by revolving the plane region about the y-axis. , , .

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Step-by-step explanation:

Given (Missing Information):

; ;

Required

Determine the volume

Using Shell Method:

First solve for a and b.

and

Substitute 8 for y

Take 2/3 root of both sides

This implies that:

For

This implies that:

So, we have:

The volume of the solid becomes:

Open bracket

Integrate

Substitute 4 and 0 for x

Take LCM

Hence, the required volume is: