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Section 7.5 Polar Arclength (CO5)

Subsection 7.5.1 Activities

Activity 7.5.1.

Recall that the length of a parametric curve is given by
t=at=b(dxdt)2+(dydt)2dt.
(a)
Let x(t)=rcos(θ) and y(t)=rsin(θ) and show that the length of a polar curve r=f(θ) with αθβ is given by
θ=αθ=β(r)2+(drdθ)2dθ.
(b)
Find an integral computing the arclength of the polar curve defined by r=3cos(θ)2 on π/3θπ.
(c)
Find the length of the cardioid r=1cos(θ).

Subsection 7.5.2 Videos

Figure 173. Video for CO5

Subsection 7.5.3 Exercises