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Step 1 :

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The equation of the wire is $\"\"$ and $\"\"$ .

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The wire density is $\"\"$ .

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Mass of the wire is $\"\"$ .

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Where $\"\"$ .

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Compare $\"\"$ with $\"\"$ .

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

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Substitute $\"\"$ and $\"\"$ in equation (1).

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$\"\"$

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

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$\"\"$

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Step 2 :

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Find mass of wire :

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$\"\"$

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Consider $\"\"$ then $\"\"$ .

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Find the new limits:

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when $\"\"$ , $\"\"$ .

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when $\"\"$ , $\"\"$ .

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Substitute the corresponding values in equation (2).

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$\"\"$

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The mass of the wire is $\"\"$ .

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Solution :

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The mass of the wire is $\"\"$ .

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