Homework SourseFind the length of the curve rtSolution length integral of
Find the length of the curve r(t)=<12t,8t^3/2, 3t^2>?
Solution
length = integral of v(dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2 dx/dt = 12, dy/dt = 12vt, dz/dt = 6t length = integral of v(144 + 144t + 36t^2) length = 6 integral of vt^2 + 4t+4) length = 6 integral of (t+2)dt integrating length = 6(t^2/2 + 2t) + C length = 3t^2 + 12t + C
