Identify the integral used to determine the surface area of the surface of revolution for the shape described by , , revolved about the x-axis.

Question

Identify the integral used to determine the surface area of the surface of revolution for the shape described by  ,  , revolved about the x-axis.

Quizplus · Accepted Answer

The integral used to determine the surface area of the surface of revolution for the shape described by the given curves revolved about the x-axis is:

A = 2π∫[a,b] y √(1 + (dy/dx)^2) dx

In this case, y = 11e^(ax), so dy/dx = 11a e^(ax). Substituting these values, we get:

A = 2π∫[0,1] 11e^(ax) √(1 + (11a e^(ax))^2) dx

Integrating this expression will give us the surface area of the surface of revolution. Solving the integral, we get the answer as option C:

A = 2π/11a [(1 + 11a^2)^(3/2) - 1] from a=0 to a=1, which simplifies to:

A = 2π/11 [(1 + 11^2)^(3/2) - 1]

Identify the Integral Used to Determine the Surface Area of the Surface