Answer to Question #2208 in Calculus for lune
2011-03-30T04:19:04-04:00
Estimate the arc length of r(t) = (cos^2 t, sin 3t), t element of [0, pi] using trapezoidal rule with n = 6.
1
2011-06-22T09:47:22-0400
Divide the interval in n parts. Find distance between every pair of two nearest points. t 0 π/6 π/3 π/2 2π/3 5π/6 π x=cos2 t 1 3/4 1/4 0 1/4 3/4 1 y=sin3t 0 1 0 -1 0 1 0 d=√((xk -xk-1 )2 +(yk - yk-1 )2 ) - √17/4 √5/2 √17/4 √17/4 √5/2 √17/4 The arc length is the sum of smaller parts: L = √17/4 + √5/2 + √17/4 + √17/4 + √5/2 + √17/4 = √17 + √5 ≈ 6.3592
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