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Find the length of the curve: {eq}y = \ln(\sec x) {/eq} from {eq}x = 0 {/eq} to {eq}x = \frac{\pi}{4} {/eq}.

Question:

Find the length of the curve: {eq}y = \ln(\sec x) {/eq} from {eq}x = 0 {/eq} to {eq}x = \frac{\pi}{4} {/eq}.

Length of Curve:

The length of the curve can be found by using the formula {eq}L=\int_{a}^{b}\sqrt{1+y'^{2}}dx {/eq} where we will differentiate the curve and then plug-in the values in the formula and then plug in the upper and lower bounds.

Answer and Explanation: 1

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To solve the length of the curve we will proceed as

{eq}L=\displaystyle\int_{a}^{b}\sqrt{1+y'^{2}}dx {/eq}

where a,b is the interval

{eq}y=\displa...

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