Given that r(t) = 3sin(t)i + 3cos(t)j + 4(t)k. Find the length of the curve...

Question

Given that r(t) = 3sin(t)i + 3cos(t)j + 4(t)k.

1. Find the length of the curve for 0 < t < pi/2. Note: < is less than or equal to symbol.
2. Reparametrize the curve with respect the arc length measured from t = 0 in the direction of increasing t.

Answer 1

ds = (dx² + dy² + dz²)^1/2 = ((dx/dt)²+ (dy/dt)² + (dz/dt)²)^1/2 which you can work out to be 5

Integrating and setting s(0)= 0 you get s = 5t

The questions should be reasonably straightforward at this point.