Help! I can't seem to figure this out :( (Involves disk/washer method)

[Retain]

Hi there!!! I'm assuming I'm posting this in the right place, because it said post math questions here or something, if not sorry! :(.

Anyway I keep getting the wrong answer for this one question and would greatly appreciate it if someone can tell me what I'm doing wrong.

Directions:
For exercises 21-25, find the volume of the solid generated by revolving the region bounded by the graphs of the given equations about the line y=4

Question #21: y=x, y=3, x=0

The answer is 18pi but I get something else, dunno what I'm doing wrong!  Maybe I'm approaching it wrong or something.

What I did:
Well I need to find the outer and inner radius, so thats what I did!

Since it's revolving around y = 4, I made the outer radius (R) = 4, then squared 4 so it becomes 16 and integrated it using the interval [0, 3] and end up with 48pi.

For the inner radius (which I assume is the empty space), I made it = 4 - x
-4 from the outer subtracted by the line y = x at the interval [0,3]

I then square (4-x), integrate it with the interval [0,3], ending up with 21pi.

Obviously I did something wrong because 48-21 isn't 18 :(.

Any idea what I did wrong?

[Miamiandy]

outer radius is x-4. inner radius is 1. , interval from 0 to 3.

Integrate[(x - 4)^2 - 1^2, x]

pi(15x -4x^2  +(x^3)/3)

[pi(15x -4x^2  +(x^3)/3)] {x>3} - [pi(15x -4x^2  +(x^3)/3)] {x>0}

18pi

outer radius is x-4 because it is y=x is further from y=4 and x-4 is how it appears if y=4 were the x-axis. Also, inner radius is 1 because y=3 is 1 away from the rotation axis of y=4.

[Retain]

Thank you so much!!!!!!!!  ;D

[Miamiandy]

No problem.