Homework SourseFind the exact length of the curve x 6 9t2 y 6 6t3 0
Find the exact length of the curve.
x = 6 + 9t^2
y = 6 + 6t^3
0<=t<=3
x = 6 + 9t^2
y = 6 + 6t^3
0<=t<=3
Solution
dx/dt = 18t dy/dt = 18t^2 arc length = integral of sqrt[(dx/dt)^2 + (dy/dt)^2]....limit from 0 to 3 arc length = integral of sqrt[324t^2 + 324t^4] arc length = 18 * integral of tsqrt(1+t^2) integrating wrt t arc length = 18 * 1/2 * 2/3(1+t^2)^3/2 arc length = 6(1+t^2)^3/2 apply limits arc length = 6[10^3/2 - 1]
