What is the arclength of the polar curve #f(theta) = sin4theta-cos3theta # over #theta in [pi/3,pi/2] #?
The arclength is approximately
The equation for arclength of a polar curve is:
In this case,
So, the arclength can be found by:
I am not entirely sure how to solve this integral manually; if anyone else has a valid method of integration, feel free to extend this answer, but as far as I can see, the only way to solve this problem is with a graphing calculator or similar interface.