   Chapter 8.1, Problem 94E

Chapter
Section
Textbook Problem

Arc Length End the arc length of the graph of y = ln ( cos x ) from x = 0   to   x = π / 3 .

To determine

To calculate: The arc length of the given curve expressed as y=ln(cosx) over the given interval [0,π3].

Explanation

Given:

The curve is y=ln(cosx) over the interval [0,π3].

Formula used:

The arc length L along a curve y=f(x) from a to b is given by the following integral,

L=ab1+(f(x))2dx and the integration formula is secxdx=ln|secx+tanx|+C.

Calculation:

Consider the given function expressed as,

f(x)=ln(cosx)

Now, take the derivative of the function above to get,

f(x)=sinxcosx=tanx

Therefore, length of the arc is,

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