This week in calculus i started off being confused by Volume of Disks and Washers, but on Friday, Mrs. Robinson gave us a packet to practice these concepts with and i must say that the packet helped me tremendously.
Volume by Disks:
when dealing with disks, your fourmula will be pie times the function they give you squared. for example, lets say that you are given the formula x^2 +2x and they want the volume by disks, you would square the function which would give you 4x^3 +6x^2. Then you would integrate the function and plug in your bounds... sometimes they may give you the bounds so all you would have to do is plug them in.. otherwise you will either have to set the equations equal to each other or look at the graph if you are given one.
Washers:
volume by washers is basically the same concept except that it is not just one formula squared, it is pie times the top equation squared minus the bottom equation squared. You figure out which formula is the top and bottom by graphing the equation by hand or on your calculator, once you figure that out, you then square the functions and integrate them and solve. Again, the same rules apply to the bounds.
Sometimes, they will not ask you for the volume, instead they will ask you for the area of the disk or washer, if that is the case then you have to use a different function. When asked for the area, there is no pie involved and the formula is the top equation minus the bottom equation. You find your bounds the same way as the volume problems. So you would integrate the functions as usual and plug in the bounds.
Some of the things i am having problems with is the graphs. I can plug them in on my calculator and see what they look like, but i don't understand what to shade. If anyone can help me graph my equations that would be a huge help. Thanks!
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