i'm going to use x in place of theta since i don't know how to make the symbol
find the length of the cardioid r=1 + cos(x).
so first i take the derivative, which is -sin(x). that squared would be sin(x)^2
(1+cos(x))^2 is 1 +2cos(x) +cos(x)^2.
put these both under the square root symbol and take the integral of the whole thing. i apologize for my lack of proper formatting.
so we have int(sqrt(1+2cos(x)+cos(x)^2 +sin(x)^2))
the cos(x)^2 + sin(x)^2 =1, which gives:
int(sqrt(2+2cos(x)). there i am stuck, i don't know how to solve that integral. can anyone help? and did i at least make it to this point without any mistakes? please let me know wherever i messed up. also i have the limits of integration from 0 to 2pi, but i'm not very sure that is correct.