# Homework Help: Finding surface of revolution

1. Jun 28, 2011

### iqjump123

1. The problem statement, all variables and given/known data
Find the area of the surface of revolution generated by revolving about the x axis the cardioid x=2cos$\vartheta$-cos2$\vartheta$,y=2sin$\vartheta$-sin2$\vartheta$.

pictures show a cardioid with $\vartheta$=pi and $\vartheta$=0.

2. Relevant equations
After looking up, the formula to solving this type of equation is:
s=int(sqrt(dx/dtheta)^2 +sqrt(dy/dtheta)^2)
and also some trig identities

3. The attempt at a solution
Alright, I first went ahead and applied the equation above to the functions, and integrated from 0 to pi (since that is where the edges of the cartoid lie?). However, after going through the math and solving it out, I get a -2/3(sinx*cosx^3/2) from 0 to pi, which makes no sense (since volume will be 0 if this int. is evaluated).

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution