$\"\"$

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The equation of the graph is $\"\"$ on $\"\"$ .

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Find the arc length.

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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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Here $\"\"$ is $\"\"$ .

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The function is $\"\"$ .

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Diffrentiate with respect to $\"\"$ .

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$\"\"$

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Substitute $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$ .

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$\"\"$

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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 of $\"\"$ on interval $\"\"$ is $\"\"$ .

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$\"\"$

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The ellipse equation is $\"\"$ .

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$\"\"$

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$\"\"$ .

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The ceecentricity of ellipse is $\"\"$ .

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$\"\"$ .

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The circumference of the ellipse is $\"\"$ .

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$\"\"$

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$\"\"$ .

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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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$\"\"$ .

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Therefore, the arc length of $\"\"$ on interval $\"\"$ is equal to the circumference of ellipse $\"\"$ .

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$\"\"$

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The arc length of $\"\"$ on interval $\"\"$ is equal to the circumference of ellipse $\"\"$ is $\"\"$ .