Finding surface of revolution

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Homework Statement


Find the area of the surface of revolution generated by revolving about the x axis the cardioid x=2cos[itex]\vartheta[/itex]-cos2[itex]\vartheta[/itex],y=2sin[itex]\vartheta[/itex]-sin2[itex]\vartheta[/itex].

pictures show a cardioid with [itex]\vartheta[/itex]=pi and [itex]\vartheta[/itex]=0.


Homework 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

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).

thanks so much in advance!

Homework Statement





Homework Equations





The Attempt at a Solution

 

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