Obtain the volume of the solid of revolution e^-x about the x-axis using the washer or disk method.

We are given the solid of revolution formed by revolving the region bounded by e^-x, x=1, y=1/e and the y-axis about the x-axis, and we are using the washer or disk method to compute the volume of the solid. We slice the volume into washers (disks with holes) in order to set up the integral. Each washer is located at a position of x, so the outer radius of the washer is e^-x and the inner radius is 1/e. We compute the area of the washer and multiply by the thickness to obtain the volume given by the washer. Next, we add up all the volumes of the washers using integration as a summation device. We compute the definite integral and simplify the result, and we obtain the volume of the solid of revolution e^-x about the x-axis.