Explanation Given: The following curve is given, y = 1 2 x 2 … ( 1 ) over the interval [ 0 , 2 ] Formula Used: The surface area S of the solid obtained by rotating the curve y = f ( x ) over the interval [ a , b ] about the x -axis is: S = 2 π ∫ a b f ( x ) 1 + f ' ( x ) 2 d x … ( 2 ) Calculation: Consider the given equation, y = 1 2 x 2 Now, differentiating it with respect to x , we get y ' = 1 2 ⋅ 2 x = x y ' 2 = x 2 Now, 1 + [ f ' ( x ) ] 2 = 1 + [ y ' ] 2 = 1 + x 2

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Chapter 9, Problem 16CRE

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How to calculate the surface area of the solid obtained by rotating the curve over the given interval about the x-axis.

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Chapter 9, Problem 15CRE

Chapter 9, Problem 17CRE

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How to calculate the surface area of the solid obtained by rotating the curve over the given interval about the x -axis.

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