Integration is the main mathematical idea that makes this course so difficult. Most of you remember from calculus that integration finds areas under curves, or if you are really advanced, finds volumes of objects. We will use integration a lot in this course, but never to find areas or volumes (except in the second homework assignment). To survive, you will have to generalize your concept of what integration means. As explained in the long, detailed, and incredibly boring article in the student packet, integration is the process of adding up billions and billions of little bits of something to find the grand total. Little bits of mass can be added up to find the total mass; little bits of charge can be added up to find the total charge; little bits of force, electric field, voltage, current, magnetic field, etc., can all be added up via integration to find the total. Please sit down with pencil and paper and work through all of the examples in the article.
Integration problems can be incredibly difficult, and some of the homework problems will be challenging enough to force you to look some integrals up in the standard tables (CRC, Dwight, Pierce, Gradshteyn and Ryzhik). But for examinations you will only have to know the following integrals (and their cousins) from memory.
Fortunately, this table is simply the inverse of the differentiation table above. The cousins of these integrals are integrals like this:
