Solid of Revolution (RAD)

[macgophie]

Need help with working this problem on a TI-84 Plus.
y=-3 cos (2 * Pi * x)
Axis of Revolution: x = 0.2

What is the volume?

[ZachB]

Use the Shell Method for a function of a varibale that is parallel to the axis you're rotating about. So a differential unit of volume will be equal to 2*Pi*R*f(x)dx, where R is the radius of the differential unit being rotated. Here, since we are rotating about x=.2, then the radius each differential will be rotating at will be (x-.2). Now, f(x)=-3*Cos[2*Pi*x], so after plugging in values of R and f(x) we have the formula for each diffential unit of volume. In order to get the total volume, we have to add up all those little units of volume from the axis of rotation (x=.2) to where the function crosses the x-axis (x=.25). Luckily, Leibniz and Newton invented a way for us to do that and its called integration.

So type your differential volume formula into the "y=" part of the calculator so it reads:

y=2*Pi*(x-.2)(-3Cos[2*Pi*x])

from the calculate menu ([2nd] [trace]), use option number seven, which is integrate function. It will ask for the lower limit of integration, which is .2, and then it will ask for the upper limit, which is .25. It will return a value to the bottom of the screen which is the answer.

[macgophie]

Amazing! Thanks for the help!