For rotation about the x - axis, the surface area formula : $\"image\"$ .

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For rotation about the y - axis, the surface area formula : $\"image\"$ .

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The rotating curve y = √(1 + 3x) about the x - axis and the interval [a, b] = [1, 9].

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y = √(1 + 3x) ⇒ y\\' = 3/[2√(1 + 3x)]

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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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Apply formula : $\"\"$ .

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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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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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Therefore, area of the surface obtained by rotating the given curve about the x - axis is $\"\"$ .

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