Find the volume of the solid formed by rotating the region enclosed by

Question

y=e^2x+5 y=0 x=0 x=0.4
about the x-axis.

Answer 1

v = ∫[0,0.4] πr^2 dx
where r = y = e^2x
v = ∫[0,0.4] π e^(4x) dx
= 1/4 π e^(4x) [0,0.4]
= π/4 (e^1.6 - 1)