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Length of Polar Curve Help Please?
Length of Polar Curve Help Please?
Find the exact length of the polar curve described by: r=2e^.4theta on the interval [0,(1/6)]? Please write decimal answer.
Please Help.
2 Answers
- Anonymous9 years agoFavourite answer
cut a length dl on the curve
then dl = rdθ
dl = 2e^4θdθ
integrate from 0 to 1/6
l = 2. e^4θ/4|0 to 1/6
= 0.5(e^4/6 - 1) = 0.5 x 0.95 = 0.477
- orsolaLv 44 years ago
For parabolic coords (A,B) and cartesian (x,y) x = AB y = (a million/2 of)*(B^2-A^2) arc length: s = r(theta) r=sqrt(x^2+y^2) theta = arctan(y/x) so, arc length = sqrt(x^2+y^2)*arctan(y/x) = sqrt((AB)^2+(a million/2)*(B^2-A^2)y^2)* arctan((a million/2)*(B^2-A^2)y/AB) that is often simplified to tidy it up (sorry havent gained time at mo!)
