Question

Find the exact length of the curve.
x = 1 + 9t^2, y = 3 + 6t^3, 0 ≤ t ≤ 5

Answer 1

\[
L = \int_0^5\sqrt{\left(\frac{dx}{dt}\right) ^2 + \left(\frac{dy}{dt}\right)^2}dt
\]

Answer 2

how do you proceed from there?

Answer 3

You are given x as a function of t. Find dx/dt
Then find dy/dt. Plug it into above equation, integrate, and put in the upper and lower bounds.