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:

answer: there are x+184 pages in olivia's book.

step-by-step explanation:

let the total number of pages in the book which olive has already read be x.

then if olive has 184 pages left to read, then the total number of pages are in olive's book= pages she has read+pages she has left to read

therefore, the total number of pages in olivia's book=

hence, there are x+184 pages in olivia's book.