Find the volume of the solid formed by rotating the region enclosed by y=e2x+1, y=0, x=0, x=0.9 about the y-axis.

Answer 1

fix your typing before we attempt this

is it
e^(2x) + 1 or e^(2x+1) ?

Answer 2

Break the area into two regions:

from y=0 to y=1, which becomes a cylinder of radius .9, height=1.

Integrate on x, using shells

∫[0,.9] 2πx(e^2x+1 - 1) dx
= 2π∫[0,.9] xe^2x dx
= π/2 e^2x (2x-1) [0, .9]
= . . .