Arc length of a polar curve
Favorites|Homepage
Subscriptions | sitemap
HOME > > Arc length of a polar curve

Arc length of a polar curve

[From: ] [author: ] [Date: 12-06-27] [Hit: ]
So,= ∫(w = 0 to π) |cos w| * 2 dw, letting w = θ/2.= 2 * ∫(w = 0 to π/2) +(cos w) * 2 dw,= 4.I hope this helps!......
Find the exact length of the polar curve r=cos^2(theta/2)

Pleeeease help!

-
Note that the entire curve is plotted for θ in [0, 2π].

Plot:
http://www.wolframalpha.com/input/?i=pol…
------------------------
So, the arc length ∫ √(r^2 + (dr/dθ)^2) dθ equals
∫(θ = 0 to 2π) √[(cos^2(θ/2))^2 + (-cos(θ/2) sin(θ/2))^2] dθ
= ∫(θ = 0 to 2π) |cos(θ/2)| √[cos^2(θ/2) + sin^2(θ/2)] dθ
= ∫(θ = 0 to 2π) |cos(θ/2)| * 1 dθ
= ∫(w = 0 to π) |cos w| * 2 dw, letting w = θ/2.
= 2 * ∫(w = 0 to π/2) +(cos w) * 2 dw, via symmetry
= 4 sin w {for w = 0 to π/2}
= 4.

I hope this helps!
1
keywords: curve,Arc,polar,length,of,Arc length of a polar curve
New
Hot
© 2008-2010 http://www.science-mathematics.com . Program by zplan cms. Theme by wukong .