$\"\"$

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The function is $\"\"$ and the interval is $\"\"$ .

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(a)

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Graph :

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(1) Draw the coordinate plane.

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(2) Graph the function $\"\"$ .

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$\"\"$

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Observe the graph :

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The pink colour represents the function $\"\"$ .

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The green colour represents the arc length of the curve over the interval $\"\"$ .

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$\"\"$

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(b)

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Definition Of Arc Length :

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Let the function given by $\"\"$ represent a smooth curve on the interval $\"\"$ .

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The arc length of $\"\"$ between $\"\"$ and $\"\"$ is $\"\"$ .

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Where $\"\"$ is $\"\"$ .

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The function is $\"\"$ .

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Diffrentiate with respective to $\"\"$ .

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$\"\"$

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$ .

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$\"\"$

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(c)

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The arc length is $\"\"$ .

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Consider the integrand $\"\"$ on $\"\"$ .

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Graph the function $\"\"$ on $\"\"$ . \ \

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$\"\"$

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Observe the graph:

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$\"\"$ .

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The arc length is $\"\"$ .

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$\"\"$

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(a)

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The graph of the function $\"\"$ :

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$\"\"$

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(b) The arc length is $\"\"$ .

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(c) The arc length is $\"\"$ .