Hello. I need help with a problem.
The problem is: Show that the circumference of the unit circle is equal to
2 (integral, 1, -1) dx/sqrt(1-x^2) (an improper integral). Evaluate, thus verifying that the circumference is 2pi.
This is how far I've gotten:
x^2 + y^2 = 1 --> y = sqrt(1-x^2)
y = sqrt(1-x^2)
(y')^2 + 1 = (-x/sqrt(1-x^2))^2 + 1
= (x^2)/(1-x^2) + 1
Arclength = s = (integral, 1, -1) sqrt(1 + (x^2)/(1-x^2)) dx
= (integral, 1, -1) sqrt(1/(1-x^2)) dx
This is where I am stuck. Thanks!