🔗 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 α≤θ≤β 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/3≤θ≤π. 🔗(c) 🔗Find the length of the cardioid .r=1−cos(θ).
🔗(a) 🔗 🔗Let x(t)=rcos(θ) and y(t)=rsin(θ) and show that the length of a polar curve r=f(θ) with α≤θ≤β 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/3≤θ≤π.