Answer to Question #184945 in Civil and Environmental Engineering for John Prats

Question

Calculate the length of the polar curve r=1-sin(theta) on the given interval (0, 2π).

Answer 1

length of an arc $l$ =$\int\limits_a^b \sqrt{{r' (}\theta)^2 + r(\theta)^2 d\theta}$

where $r = 1 -sin\theta$

and $r' =(1-cos )^2$

then $l=$ $\int\limits_a^b \sqrt{(1-cos )^2 + (1 -sin\theta)^2}$

where $a =0$ and $b= 2\pi$

$l=$ 6.283183