Find the volume v of the solid obtained by rotating the region bounded by the given curves about the specified line. y = ln(6x), y = 4, y = 6, x = 0; about the y-axis step 1 we will use horizontal strips. such a strip has a vertical span of δy. sketch the region.

V = 2219.08π

Step-by-step explanation:

If you use the washer/disk method as you indicated you were going to in the statement "we will us horizontal strips", you have to solve that equation for x.  The equation solved for x is

The bounds are y-intervals from 4 to 6, and we are rotating about the y-axis.  I cannot sketch the graph for you here, but if you need it, graph y = ln(6x) and you'll see what it looks like.  I can only help you with the calculus of it, not the drawing of it.

The volume formula then for this is

Squaring what's inside the parenthesis gives you:

To make this a tiny bit simpler we can pull out the fraction:

The antiderivative of e to the 2y power is found:

from 4 to 6

We can then pull out the 1/2:

from 4 to 6.

Evaluating that antiderivative using the First Fundamental Theorem of calculus gives you:

which simplifies to

If you leave your answer in terms of pi it is:

2219.08π or if you multiply pi in it is:

6971.44863