The arch y= sin(x), x is in [0, pi], is revolved around the line y=c, where c is a constant in [0, 1], to generate a solid...
Anyway, then I have to represent the volume of the solid as a function of c and other stuff.
The Attempt at a Solution
I remember asking in class and the proff said not to find the points of intersection with c.
The volume of the solid would be the integral of sin(x)^2 - c^2 from x=0 to x=1.
OR the integral of c^2 - sin(x)^2, x=0--->1.
Either way, there are values of x for which sin(x) is larger than c, and some where it is smaller. And either way, there are values of c for which I get a negative number, which makes no sense. What am I doing wrong? I can't think of any way of doing this without finding the intercepts, which is said specifically not to do.