Hours I spent in Calc II class this semester_ roughly 75
Hours I spent on Calc II homework/studying: roughly 150
Things I remember after only 9 days out of school_ 2
1) Pendulum clocks swing in cycloidal arcs, so the distance travelled by the pendulum dosen't matter. A well designed one always takes 1 second to swing from one endpoint to the other.
2) If you graph the curve of 1/x on the interval from 1 to infinity, it stretches infinitely far to the left and approaches, but never reaches zero as the line goes to infinity. This is basic calc 1_
If this line is rotated around the x-axis, you get a horn-shaped solid of revolution. This is also nothing new.
Through integration, we can find the volume of this integral (and it is exactly 2*Pi). This means that the volume of this surface is finite, but the surface area is infinite, since the line 1/x stretches infinitely far.
Put in real world terms, you could easily fill the shape up with the right amount of paint, but you could never produce enough paint to cover it's surface.
Things like this are why I don't believe in the religion of math.