This week all we did was learn the things that made up section 7.3 which was Solids of revolution. We learned both the disk method and the washer method.
The disk method uses the volume equation of a cylinder in a transformed way. Our equation ends up being
b
V=π ⋅ ∫[ f (x)]^2 dx
A
We can bring the pi symbol out front because it's just a constant. Then you just plug in the values for a, b, and f(x).
The washer method is almost the exact same except the equation is
B
V=π ⋅ ∫[ R(x)]^2-[ r (x)]^2 dx
A
With R(x) being the whole radius of the shape and r(x) being the little part we subtract from R(x).
I thought it was cool to start working with 3D shapes rather than just a 2D graph. At first both of these concepts were difficult for me, but as we worked in groups I started to better understand what we were doing. The picture I have added to this blog is one of my group pictures. We all worked together to understand what we were doing when we really didn't know what we were doing in the first place.
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