Find the exact length of the curve

Calculus
Tutor: None Selected Time limit: 1 Day

Find the exact length of the curve.

x = 3 + 9t2,    y = 6 + 6t3,    0 ≤ t ≤ 4

Apr 3rd, 2015

dx/dt = 18t

dy/dt = 18t2

(dx/dt)2+(dy/dt)2 = 182 t2 (1+t)2

Sqrt (182 t2 (1+t)2 = 18t √(1+t)= 18 (1+t)3/2 -18(1+t)1/2

Integrating between t= 0 to 4

18 (1+t)5/2 /(5/2) -18(1+t)3/2 /(3/2) = 18*2/5 *55/2-18*2/5 -18*2/3 * 53/2 +18*2/3

= 36/3 -36/5+ 36/5 * 55/2-36/3 * 53/2 = 72/15+36 * 53/2-12* 53/2 = 24/5+24 * 53/2


Apr 3rd, 2015

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