The given curve is rotated about the y-axis. Set up, but do not evaluate, an integral for the area of the resulting surface by integrating (a) with respect to x and (b) with respect to y.x = e3y,    0 ≤ y ≤ 2(a)Integrate with respect to x.e6 (2πx)(√109​) 1 dx(b)Integrate with respect to y.2 π·(e3y)2 0 dy

The given curve is x = e^(3y), with 0 ≤ y ≤ 2. We are rotating this curve about the y-axis and we want to find the surface area of the resulting solid.

The formula for the surface area of a solid of revolution, when rotating about the y-axis, is given by:

A = 2π ∫[from a to b] x * sqrt(1 + (dx/dy)^2) dy

(a) Integrating with respect to x is not applicable in this case because we are rotating the curve about the y-axis. The integral should be with respect to y.

(b) Integrating with respect to y:

First, we need to find dx/dy. Since x = e^(3y), dx/dy = 3e^(3y).

Then, we substitute x and dx/dy into the formula:

A = 2π ∫[from 0 to 2] e^(3y) * sqrt(1 + (3e^(3y))^2) dy

This is the integral you need to compute to find the surface area. However, the problem states to set up the integral, not to evaluate it. So, we stop here.