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

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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.

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Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 8

Further Applications of Integration

Section 1

Arc Length

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Video Transcript

it'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'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're looking at the interval zero and pi and co seek it. It'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'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'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'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.

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Problem

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

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Calculus: Early Transcendentals

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Watch More Solved Questions in Chapter 8

Video Transcript

James Stewart

Calculus: Early Transcendentals

Heather Zimmers

Caleb Elmore

Samuel Hannah

Michael Jacobsen

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Calculus: Early Transcendentals

Heather Zimmers

Caleb Elmore

Samuel Hannah

Michael Jacobsen

James StewartCalculus: Early Transcendentals

Heather Zimmers

Caleb Elmore

Samuel Hannah

Michael Jacobsen

James Stewart

Calculus: Early Transcendentals