find the surface area of the following curve rotated about the y-axis: x=e^(y/2)+e^(-y/2), -2≤y≤2

Question

I cant seem to get any answer.

Answer 1

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.