Question #184945

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

Expert's answer

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

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