Solution
If the curve y = f(x), a≤x≤b is rotated about the x-axis, then the surface area is given by
A=2π∫abf(x)1+[f′(x)]2dx
In this case f(x) = 1/3 x³, f’(x) = x2 ,a = 0, b = 2
A=2π∫0231x31+x4dx
Substitution y = x4
A=6π∫0161+ydy=9π(1+y)3/2∣016=9π(173/2−1)=24.118
Answer
A=9π(173/2−1)=24.118
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