A region R is enclosed by y = -e^{x}, y =0, x = 4 and x = 0. Rotate this about the y-axis, and find volume.

I actually have the solution worked out for this for y = +e^{x}, but I would like to know what difference does it make when it is reflected about the y-axis (ie. y = -e^{x}).

Question

A region R is enclosed by y = -e^{x}, y =0, x = 4 and x = 0. Rotate this about the y-axis, and find volume.

I actually have the solution worked out for this for y = +e^{x}, but I would like to know what difference does it make when it is reflected about the y-axis (ie. y = -e^{x}).

anonymous · Answer

No difference. By Symmetry about the x-axis, the rotated area is the same and the volume should be the same. Draw a picture and see for yourself.