Solving for Volume Using the Shell Method

[whatlifeforme]

Homework Statement

use the shell method to find the volumes of the solids generated by revolving the region about the indicated axis.

Homework Equations

x=18(y^2 - y^3) about line y=8/5.

The Attempt at a Solution

2∏∫ (0 to 1) (8/5 - y) (18y^2 - 18y^3)

 

[HallsofIvy]

Homework Statement

use the shell method to find the volumes of the solids generated by revolving the region about the indicated axis.

Homework Equations

x=18(y^2 - y^3) about line y=8/5.i

This single equation does not define a bounded region. Was there some other line or curve given, such as the y-axis (x= 0)?

The Attempt at a Solution

2∏∫ (0 to 1) (8/5 - y) (18y^2 - 18y^3)

 

[whatlifeforme]

according to the graph it appears bounded by y-axis. (x=0)

 

[Mark44]

Assuming that the region to be revolved is between one arch of the curve and the y-axis, your setup looks fine, except that you are missing the differential. It might not seem important now, but when you learn more techniques of integration, omitting the differential will be a big problem.

2∏∫ (0 to 1) (8/5 - y) (18y^2 - 18y^3) dy[/color]

What do you get for the value of your integral?