I had a question concerning the Surface area of a curve being rotated.
Question: rotate the curve (e^x) on the interval [0,1] and calculate the surface area.
I know how to set up an integral and such, but what i don't understand is would it matter if the curve e^x was bounded to y=1? Would that change the surface area like it would in volumes?
Also, what i don't understand is why can we calculate the area in terms of either "y" or "x," their derivatives give us different tangent lines don't they?
for X -> 2pi∫ e^x(sqrt(((e^x))^2)+1))dx from 0 to 1
for Y -> 2pi∫ y(sqrt(((1/x)^2)+1))dy from 1 to e