What is the ranking in oxidation between a double bonded carbon and a carboxyl carbon?
Carbon is most oxidized as a carboxyl carbon. This is due to having three of its bonds made with oxygen. Since a double bonded carbon has two bonds attached to carbon, it is slightly more oxidized that a single bonded carbon, but it is far more reduced than a carbon attached to any oxygen. In fact, carboxyl groups are some of the most oxidized groups to be found and make great electrophiles as a result.
What is the difference between an ionic and a covalent bond?
In its simplest form, an ionic bond is made between a metal and a non-metal, where the metal donates its electron(s) to become positive, and the non-metal accepts those electrons to become negative. Since the two atoms are now charged, they become ions, and are attracted to each other due to the opposing charges. A covalent bond is where [generally] two non-metals share electron(s) and become attached through their electron clouds.
What is an integral and how does it pertain to a graph?
An integral is the infinite sum of portions of the area under the curve. It is made up of many portions, defined as differentials, and can be roughly estimated through many techniques using a finite number of sums.