The region bounded by y=e^(-x^2),y=0 ,x=0 ,x=1 and is revolved about the y-axis. Find the volume of the resulting solid.

Answer 1

better use shells for this.

v = ∫[0,1] 2πrh dx
where r = x and h = y = e^(-x^2)
v = π∫[0,1] 2xe^(-x^2) dx
= π(-e^(-x^2)) [0,1]
= π(1 - 1/e)