Find the volume of the solid formed by rotating the region enclosed by y = e 5 x + 2 , y = 0 , x = 0 , x = 1 about the y-axis.

Answer 1

v = 2π∫₀¹x(e^5x + 2)dx = 155.7

This integral you can take by parts before spliting on 2 integrals: u = x; dv = e^5xdx