Use the method of cylindrical shells to find the volume v generated by rotating the region bounded by the curves about the given axis. y = 8ex, y = 8e−x, x = 1; about the y-axis

See attachment for one such shell. The volume is given by the sum of infinitely many thin shells like this, each with radius and height determined by the vertical distance between the upper blue curve and the lower orange curve for any given , i.e. .

The volume is then

What mathematical statement is missing ? ? the answer is b