Question

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.

y = ln 5x, y = 4, y = 6, x = 0; about the y-axis

V =

Answer 1

π∫52(ey3)2dy

The work I did to solve this equation:

Step 1

ln(3x)=2

3x=2e

x=2e3

Step 2

ln(3x)=5

3x=5e

x=5e3

Step 3

y=ln(3x)⟺ey=3x⟺ey3=x

Step 4

π∫52(ey3)2dy