\"\"

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

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(a)

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When \"\" then \"\".

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When \"\" then \"\".

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The end points of the arc are \"\" and \"\".

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Distance between the two points formula: \"\".

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\"\"

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\"\" units.

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\"\"

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(b)

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Find the lengths of four line segments connecting the points on the arc when \"\", \"\" and \"\".

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The points on the arc are \"\" and \"\".

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Distance between the two points formula: \"\".

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Length of first line segment joining \"\" and \"\".

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\"\".

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Length of second line segment joining \"\" and \"\".

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\"\".

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Length of third line segment joining \"\" and \"\".

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\"\".

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Length of fourth line segment joining \"\" and \"\".

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\"\".

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Find the sum of four lengths.

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\"\"

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\"\" units.

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\"\"

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(c)

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Definition of the arc length:

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If the curve \"\", \"\", then the length of the curve is defined as,

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\"\".

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\"\".

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Differentiate on each side with respect to \"\".

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\"\".

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Substitute \"\" and \"\" in \"\".

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\"\"

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Use simpson\"\"s rule with \"\" to find the value of the integral.

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The Simpson\"\"s Rule for approximating \"image\" is given by

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\"\",

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where \"image\" and  \"\"

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Here \"\", \"\" and \"\".

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\"\"

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\"\"

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\"\"

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Approximated arc length of the graph in the indicated interval is \"\" units.

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\"\"

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(d)

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Arc length of the graph of the function in \"\" is \"\".

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Graph the function \"\".

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Find the integral by using graphing utility over the interval \"\".

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\"\"

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Observe the graph:

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The value of the integral is \"\" units.

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\"\" units.

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The arc length of the function in the interval is \"\" units.

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\"\"

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(a) \"\" units.

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(b) \"\" units.

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(c) Approximated arc length by using simpson\"\"s rule is \"\" units.

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(d) Graphically \"\" units.

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The arc length of the function in the interval is \"\" units.