Question

The region enclosed by the curve y = ex, the x-axis, and the lines x = 0 and x = 1 is revolved about the x-axis. Find the volume of the resulting solid formed.
How do you do this?

Answer 1

assume you mean y = e^x
at x = 0, y = e^0 = 1
at x = 1, y = e^1 = e = 2.718

area of circle at x = pi e^2x
so I want integral from x = 0 to x = 1 of
pi e^2x dx
well to make it easy let z = 2x
then dx = dz/2
so
if x = 0, z = 0
if x = 1, z = 2
so I want the integral from z = 0 to z = 2 of
(1/2) e^z dz
= (1/2) e^z at z = 2 - at z = 0
=(1/2)(e^2 -1)

Answer 2

(pi/2)(e^2-1)

Answer 3

pi((e^2-1)/2)