Super Bowl Post.

So congratulations to the Saints on the win.

What can I cover...well

Volume by Discs (a disc does not have a hole in it)
pi times the integral from a to b of the equation squared.

Volume by Washers (a washer does have a hole in it)
pi times the integral from a to b of the top equation squared minus the bottom equation squared...

Area between two equations
the integral from a to b of the top equation minus the bottom equation

So...some people still do NOT realize this relationship:

Position is the integral of velocity.
Velocity is the integral of acceleration.

Acceleration is the derivative of velocity.
Velocity is the derivative of position.

If they give you the acceleration and want to know when you the particle changes directions...be smart about what to do. Think about what you need...

Well when a problem says when the particle changes...you should all know by now that you need to find the max's or min's of the position function, correct? Well how do you find max's or min's? You use the first derivative test. Well what is the derivative of position? Velocity. Wonderful.

So now that we know that we don't have to integrate all the way to position and just to velocity we just saved ourselves some time. So you would integrate the acceleration equation and solve for c then solve your equation when it is set equal to 0 so that you can find max's or min's. The max's or min's of the position function is where the particle changes directions.


Anyway, hopefully everyone is happy :-P