Question #85a7a

1 Answer
Andrea S.
Feb 20, 2018

#L=2#

Explanation:

The formula for the curve length is:

#L = int_0^pi sqrt(r^2(theta) +((dr)/(d theta))^2 )d theta#

#L = int_0^pi sqrt(sin^4(theta/2) + sin^2(theta/2)cos^2(theta/2))d theta#

#L = int_0^pi sqrt(sin^2(theta/2) (sin^2(theta/2)+ cos^2(theta/2))d theta#

#L = int_0^pi sqrt(sin^2(theta/2) )d theta#

in the interval #theta in (0,pi)# #sin(theta/2) > 0#, so:

#L = int_0^pi sin(theta/2) d theta#

#L = -2[cos(theta/2)]_0^pi = 2#

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