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The surface area can be regarded as the sum of the areas of the edges of a number of thin discs each with thickness dy and radius x. The surface area of the edge is 2(pi)xdy=2(pi)(e^(y/2)+e^(-y/2))dy between limits 2 and -2. This comes to 2(pi)[(1/2)e^(y/2)-(1/2)e^(-y/2)](2,-2)=(pi)(e-1/e-1/e+e)=2(pi)(e-1/e)=14.7680.

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