Could you clarify your notation and question? Along the unit circle, there exist numbers (specifically the entire portions of the circle in QI and QIII) such that the integrand you have provided appears to be imaginary. This can be done, but are you actually looking for a real number integral? Also, when you say "along unit circle r=1," are you asking about the line integral along the unit circle? Thanks!
Answers & Comments
Verified answer
I'm pretty sure it's zero.
Converting to polar coordinates, we'll get
∫ √ (1/2 r^3 sin(2θ) dr dθ)
But on the unit circle, dr = 0
So the whole integral becomes zero.
Could you clarify your notation and question? Along the unit circle, there exist numbers (specifically the entire portions of the circle in QI and QIII) such that the integrand you have provided appears to be imaginary. This can be done, but are you actually looking for a real number integral? Also, when you say "along unit circle r=1," are you asking about the line integral along the unit circle? Thanks!