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THe parametric equations of the curve C are:
x = a(t-sin(t)), y = a(1-cos(t))
where 0 <= t <= 2pi
Find, by using integration, the length of C.
[itex] \dfrac{dx}{dt} = a (1-\cos t) [/itex]
[itex] \dfrac{dy}{dt} = a\sin t [/itex]
[itex] \left(\dfrac{dx}{dt}\right)^2 + \left(\dfrac{dy}{dt} \right)^2 = a^2 (1 - 2\cos t + cos^2t + sin^2 t) = 2a^2(1 - \cos t)[/itex]
length of curve = [itex] S = \displaystyle\int_0^{2\pi} \sqrt{2a^2(1-\cos t)}\ dt = -2 \sqrt{2} a \left[\sqrt{1 + \cos t} \right]_0^{2\pi} [/itex]
evaluating this I get 0... any help?
x = a(t-sin(t)), y = a(1-cos(t))
where 0 <= t <= 2pi
Find, by using integration, the length of C.
[itex] \dfrac{dx}{dt} = a (1-\cos t) [/itex]
[itex] \dfrac{dy}{dt} = a\sin t [/itex]
[itex] \left(\dfrac{dx}{dt}\right)^2 + \left(\dfrac{dy}{dt} \right)^2 = a^2 (1 - 2\cos t + cos^2t + sin^2 t) = 2a^2(1 - \cos t)[/itex]
length of curve = [itex] S = \displaystyle\int_0^{2\pi} \sqrt{2a^2(1-\cos t)}\ dt = -2 \sqrt{2} a \left[\sqrt{1 + \cos t} \right]_0^{2\pi} [/itex]
evaluating this I get 0... any help?
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