Final answer:
To find the length of the curve defined by r(t) = 7it²j(t)³k, use the arc length formula and integrate with respect to t over the desired interval.
Step-by-step explanation:
To find the length of the curve defined by r(t) = 7it²j(t)³k, we can use the arc length formula:
S = ∫√(dx/dt)² + (dy/dt)² + (dz/dt)² dt
In this case, dx/dt = 0, dy/dt = 14it³, and dz/dt = 21it⁶. Substituting these values into the formula and integrating with respect to t over the desired interval will give us the length of the curve.