The region enclosed by the curve y =e^x, 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.

Answer 1

just use discs:

v = integral(pi*r^2)dx from x=0 to 1
where r = y = e^x
v = pi*Integral(e^2x dx) [0,1]
= pi(1/2 e^2x) [0,1]
= pi(e^2/2 - 1/2)
= pi/2 (e^2 - 1)