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# 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.$$r(t)=(4 \cos t) \mathbf{i}+(4 \sin t) \mathbf{j}+3 t \mathbf{k}, \quad 0 \leq t \leq \pi / 2$$

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

Vectors

Vector Functions

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##### Lily A.

Johns Hopkins University

##### Catherine R.

Missouri State University

##### Samuel H.

University of Nottingham

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### Video Transcript

function off a curb and you're us to find it's arc life perimeter and then user to find our client. So to find the art length permit, er, that's right. The formula first. Still, it will be us in terms of tea. Both the integral from zero can t equals zero to t and them speed. I'm just gonna norte speed be Tell Andy tell So this is our formula for arc length perimeter. So to find speed, we just need to take the drifter and lend tickets magnitude. So our velocity which just the first riveter imprints of P isas follows the directive A bitch competent sutra video of coastline is just negative sign so it will be negative for sign t I Plus for the writable sign is co sign Hey J and then did jury of tears History says three. Okay, so this is our derivative on then to find the speed, we just take the distance for Melo So our stay will be 16 signed square t but 16 Hussein skirt t cause night we can factor dis part out so we can factor 16 out They will be saying square of tea Oppa's course Zion square of tea and this is just one. Still, this is Route 25 which gives us five. Now we can used if given formula to find the arc length perimeter. So it will be myself. T he goes from zero to t five t tell So decisions five. I tell you, my lady, from zero to t and it's just tickles to five t So this is the first part of the question. Are parameter case despite t and then were asked to find the length following the given interval from zero to perhaps. So in this case, we'll just play King Pie. Hafs. So I saw I have logistical is too life hi over two. And this is the answer for a second part of the question.

#### Topics

Vectors

Vector Functions

##### Lily A.

Johns Hopkins University

##### Catherine R.

Missouri State University

##### Samuel H.

University of Nottingham

Lectures

Join Bootcamp