Y axis volume rotation

[sansone]

Hey! I have looked at the autograph visual demonstrations posted on the website, and have seen a section dedicated to Volume revolution around the x-axis. However, there is no mention to how to rotate the integral of a funtion around the y-axis. Does anybody know any procedure?

Thank you very much for all help!

n.b. I\'m using the 30 days trial version!

[Simon]

Hi sansome,

There are two different types of volume of revolution about the y-axis:

1. Area under x=f(y) (Discs Method)

Turn on Slow Plot
Enter Equation x = sin(y) as 2D equation
Point Mode
Add points at y = 0 and y = 2
Select both points (hold down Shift for multiple select)
Right-click > Find Area
Select the area
Right-click > Volume

2. Area under y=f(x) (Shell Method)

Turn on Slow Plot
Enter Equation y = x(x-1) as 2D equation
Point Mode
Add points at x = 1 and y = 2
Select both points (hold down Shift for multiple select)
Right-click > Find Area
Enter Equation x = 0 as 2D equation
Select the area and the line x = 0
Right-click > Volume

The Shells Method uses a more general feature available in Autograph which is the volume about an arbitrary line.  You could have created a line through two points and done the volume of revolution about that.

Hope this helps

Simon

[HeidILeonIe]

hi,
thanks so much for the instructions on y axis volume revolution, however I was wondering if there is a way to express the area  above a  graph and rotate this? so for example the area inside the "smiley" of y = x

[Simon]

Hi Heidi,

The rotation of the area between two curves is what you are after.

1. Enter y = x