Basic Integral calculus volume problem

[Adam111]

Hi everyone, this is my first time posting on these forums. If I am doing anything wrong, please let me know.


I am having a lot of trouble with conceptualizing rotating lines around the X- and Y-axis.

The problem I am trying to visualize right now is...

Using integrals to represent the volume of the solid formed by...

Y = sqrt(x)+3, Y = 7 - (1/2)x, and the Y-axis. Rotated around the line Y = 3.

my gut feeling for this problem is...

To setup the integral so that it looks like this...

setting the two equations equal, and differentiating for X, the integral is from [0,4]

and this is then my integral setup.

(Pi(7 - (1/2)x - 3)^2 - Pi(sqrt(x) + 3 - 3)^2)DX

This creates a washer with outer radius of Pi(4 - 1/2x)^2 and inner radius Pi(x)


I am pretty new to calculus, and I understand this is a very basic concept.
I am just looking for some pointers on how to approach these kinds of problems.

and is this even a correct way to solve this problem?

 

[Dick]

If you are new to this stuff, then you are way ahead of the curve. That looks good to me.