a-find-the-arc-length-function-for-the-curve-y-ln-sin-x-0-x-pi-with-starting-point-fracpi2-0-b-graph

Question

(a) Find the arc length function for the curve $ y = \ln (\sin x) $, $ 0 < x < \pi $, with starting point $ ( \frac{\pi}{2}, 0) $.
(b) Graph both the curve and its arc length function on the same screen.

Clarissa Noh · Accepted Answer

it&#x27;s clear, so immune right here. So we have. Why is equal to Ellen of Sign So D why over the hex is equal to one over sign Oren&#x27;s co sign with juice Co tangent. And so when we do one plus do you Why, over t X square is this equal to those seeking square? Just equal to the absolute value of CO Speaking of X So we&#x27;re looking at the interval zero and pi and co seek it. It&#x27;s bigger than or equal to zero. So we have this to be equal to coast seeking of X. We have to substitute into our art length function which gives us t is equal to pax. I&#x27;m t is equal to Pi house Cool Seaton of tea E t which is equal to l on, of course, seeking of tea minus co tangent of tea. We&#x27;re finding it when t is equal to x and T is equal to Pi house. This gives us help then of co Seacon Thanks minus co tangent of tea What engine of X And since coast seeking it is bigger or equal to co tangent for access between zero and pi s of X is equal to Ellen Co Seacon of X minus co Tangent of vets. Next, we&#x27;re going to graft the curve on the Ark link function. So first do our well and ah, sign of X in black. So I look something like this. This is a rush trying. And then our second function. Well, look, something like this.

Problem

Find the arc length function for the curve $ y = …

Problem 36 Hard Difficulty

(a) Find the arc length function for the curve $ y = \ln (\sin x) $, $ 0 < x < \pi $, with starting point $ ( \frac{\pi}{2}, 0) $.
(b) Graph both the curve and its arc length function on the same screen.

Answer

a) $L(x)=\ln |\csc x-\cot x|$
b) The black curve represents the curve $y=\ln (\sin x)$
The blue curve represents the length function
The red dot is the starting point $\left(\frac{\pi}{2}, 0\right)$

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Video Transcript

Calculus: Early Transcendentals

Grace H.

Anna Marie V.

Caleb E.

Samuel H.

Integration Review - Intro

Definite vs Indefinite

a) $L(x)=\ln |\csc x-\cot x|$b) The black curve represents the curve $y=\ln (\sin x)$The blue curve represents the length functionThe red dot is the starting point $\left(\frac{\pi}{2}, 0\right)$

Calculus: Early Transcendentals

Grace H.

Anna Marie V.

Caleb E.

Samuel H.

Integration Review - Intro

Definite vs Indefinite

Grace H.

Anna Marie V.

Caleb E.

Samuel H.

a) $L(x)=\ln |\csc x-\cot x|$
b) The black curve represents the curve $y=\ln (\sin x)$
The blue curve represents the length function
The red dot is the starting point $\left(\frac{\pi}{2}, 0\right)$