Answered: Find the length of the arc if f(x) =…

Find the length of the arc if f(x) = In(cos x) and 0 s x %3D 2. Find the length of the arc formed by x (y-1) in the interval 2 sys 9. %3D

Intermediate Algebra

10th Edition

ISBN:9781285195728

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter8: Conic Sections

Section8.2: More Parabolas And Some Circles

Problem 63.2PS: By expanding (xh)2+(yk)2=r2, we obtain x22hx+h22ky+k2r2=0. When we compare this result to the form...

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Question

I need help with both questions please

1.
Find the length of the arc if f(x) = In(cos x) and 0 s x
%3D
2.
Find the length of the arc formed by x (y-1) in the interval 2 Sys9.

Expert Solution

Part(1) Step 1

NOTE: Refresh your page if you can't see any equations.

$y=\ln \left(\cos \left(x\right)\right)$

take derivative

$y'=\frac{d}{dx}\left(\ln \left(\cos \left(x\right)\right)\right)$

$y'= \frac{1}{\cos \left(x\right)}\frac{d}{dx}\left(\cos \left(x\right)\right)$

$y'= \frac{1}{\cos \left(x\right)}\left(-\sin \left(x\right)\right)$

$y'= -\frac{\sin \left(x\right)}{\cos \left(x\right)}$

$y'= -\tan \left(x\right)$

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