Find the length of the curve r = cos^2(theta/2)

[Manni]

Find the length of the curve r = cos^2(theta/2)

I'm hopelessly lost.

 

[jedishrfu]

consider a simpler case y=x^2 and what is the length from x=0 to x=10?

dlen = (dx*dx + dy*dy) ^ (1/2) based the pythagorian theorem

and dy= 2xdx

so dlen = ( dx*dx + 4x^2 dx*dx ) ^ (1/2) = (1 + 4x^2) dx

then integrate over x to get the solution

In your equation you must consider polar coordinates so that the dlen element is:

dlen = ( dr^2 + (r*dtheta)^2 ) ^ (1/2)

plugin for dr and r and integrate over theta to get the length

 

[Manni]

Thanks a lot, makes more sense! Forgive my ignorance by the way.