- #1
Chiborino
- 21
- 0
Homework Statement
Find the arc length of the curve described by the parametric equations: x=2e^t & y=3e^3t/2 ln3≤t≤2ln3
Homework Equations
S = ∫(a->b) √[(dy/dt)^2 + (dx/dt)^2]dt
The Attempt at a Solution
Differentiated the two parametrics:
dy/dt = 2e^t
dx/dt = (3/2)*3e^3t/2 = (9/2)e^3t/2
Plugged it all in and got:
∫(ln3->2ln3) √[(2e^t)^2 + ((9/2)e^3t/2)^2]dt
= ∫(ln3->2ln3)√[(4e^2t + (81/4)e^3t]dt
I'm stuck at this integral, I don't see any viable choice for u, and I don't think I'm allowed to approximate it.
*sorry about the sloppy bound notation.