Originally Posted by
chiro Hey Hearts.
You are using the wrong variable if you are rotating about the y-axis - it should be a function of y not a function of x if you are indeed rotating it about the x-axis.
The derivative factor will also have to change meaning you will be looking at dx/dy not dy/dx since the slopes will be different.
If you can state the formula you are using it would be appreciated - otherwise you will have to state how you got it. You are correct in that you will have to take the arc-lengths of each cross section and sum them to get the surface area [which is sort of what the integral is looking to do].
If you took an arc-length approach you should get a lot of circles with varying cross sections that have their origin at the y-axis and you sum them up. If you do the arc-length approach you can introduce an argument of theta from 0 to 2*pi and make that a function of y and use that to get the area.
I'll wait for your response.