$\"\"$

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The curve equation is $\"\"$ .

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(a)

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Graph the curve equation: $\"\"$ .

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Graph:

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$\"\"$

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$\"\"$

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(b)

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Formula 3:

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Length of the curve $\"\"$ on the interval $\"\"$ is $\"\"$ .

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The curve equation is $\"\"$ .

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$\"\"$

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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The length of the curve between $\"\"$ to $\"\"$ .

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Integrate between $\"\"$ to $\"\"$ .

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$\"\"$

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Substitute $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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Since the integral is undefined at $\"\"$ , the integral is improper integral.

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$\"\"$

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Let $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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When $\"\"$ , $\"\"$ .

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When $\"\"$ , $\"\"$ .

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

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$ .

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$\"\"$

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Formula 4:

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Length of the curve $\"\"$ on the interval $\"\"$ is $\"\"$ .

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The curve equation is $\"\"$ .

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$\"\"$

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$\"\"$ .

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The length of the curve between $\"\"$ to $\"\"$ .

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Therefore, consider $\"\"$ .

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$\"\"$

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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Integrate between $\"\"$ to $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Let $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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When $\"\"$ , $\"\"$ .

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When $\"\"$ , $\"\"$ .

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

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$ .

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$\"\"$ .

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$\"\"$

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(c) Find the length of the curve from $\"\"$ to $\"\"$ .

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The curve equation is $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

Therefore, consider $\"\"$ .

\

$\"\"$

\

Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$ .

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Length of the curve between $\"\"$ to $\"\"$ is sum of length of curve between $\"\"$ to $\"\"$ and $\"\"$ to $\"\"$ .

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$\"\"$ .

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Consider $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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Let $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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When $\"\"$ , $\"\"$ .

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When $\"\"$ , $\"\"$ .

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

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$\"\"$

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$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

$\"\"$ .

\

$\"\"$

\

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

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$\"\"$

\

$\"\"$

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$\"\"$ .

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The length of the curve between $\"\"$ to $\"\"$ is $\"\"$ .

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$\"\"$

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(a) Graph the curve equation: $\"\"$ .

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$\"\"$

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(b)

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Using formula 3:

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$\"\"$ is an improper integral.

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$\"\"$ .

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Using formula 4: $\"\"$ .

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(c) The length of the curve between $\"\"$ to $\"\"$ is $\"\"$ .