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Problem 11 Easy Difficulty

Find the are length parameter along the curve from the point where $t=0$ by evaluating the integral
$s(t)=\int_{0}^{t}|\mathbf{v}(\tau)| d \tau$
from Equation (3). Then use the formula for $s(t)$ to find the length of the indicated portion of the curve.
$$r(t)=(4 \cos t) \mathbf{i}+(4 \sin t) \mathbf{j}+3 t \mathbf{k}, \quad 0 \leq t \leq \pi / 2$$

Answer

$$s(t)=5 t, \quad L=\frac{5 \pi}{2}$$

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Video Transcript

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