**Unformatted text preview: **x i , and the surface area integral becomes Z b a 2 πx p 1 + ( f ± ( x )) 2 dx. EXAMPLE 9.39 Compute the area of the surface formed when f ( x ) = x 2 between 0 and 2 is rotated around the y-axis. We compute f ± ( x ) = 2 x , and then 2 π Z 2 x p 1 + 4 x 2 dx = π 6 (17 3 / 2-1) , by a simple substitution....

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