Question

Set up integral to find the volume when region bounded by f(x)=x^2+4 and g(x)=x+4 is spun around the x-axis. Don't
evaluate.

Answer 1

did u try to sketch it ?

Answer 2

I strongly suggest that you draw this situation, showing what the solid will look like.
to determine the limits of integration, you'll need to determine where these two different "curves" intersect. How does one do that? Please use the Draw utility, below, if possible.

Next, think about which method of finding the volume would be best suited to this particular situation: disks? washers? shells? Why?

Answer 3

@mathmale , why u always give long answers ??? to explain ?

Answer 4

@BSwan: What kind of question is that, and what's your motivation for asking it? My goal is to suggest approaches that will help others solve their own problems.

Answer 5

sorry @mathmale if you felt it like criticism
my motivation is tying to see all methods of teaching

Answer 6

I'm afraid your two posts, above, @BSwan, are more distracting than they are helpful. It's just coincidence that you and I both asked AP_Calculus whether he/she had graphed the situation he/she had described. Let it be.

Answer 7

I graphed the equation and attached it below; I believe the disk method would be best.

Answer 8

Why do you choose disk method here?

Answer 9

Would the washer method be better?

Answer 10

I think we want washer method, because we have an outer and an inner radius.
Consider what this looks like when we revolve it around the x-axis. It is not touching the x-axis, it swings around an orbit around it.


Technically disk method is a washer method where the inner radius is 0.

Answer 11

Another way to interpret it is that, we find the volume of the outer radius (the line) revolved around the x-axis, and "hollow" out the part where the parabola revolves.
\( \pi R^2 \ dx- \pi r^2\ dx \)

Answer 12

Okay, I worked it and got pi(x^2+4)^2dx-pi(x+4)^2dx....then I came up with the integral of pi(x^2+4)^2-pi(x+4)^2 from 0 to 1. Would the volume be 4.61?