Area, Volume, and Arc Length explanations, examples, practice problems. Ready? Let's do this.
Area
We need to learn to slice flat food first. After it's been de-boned, a fish such as salmon is relatively flat.If we're planning on making fish sticks (we totally are), we'll need to cut that salmon...
Integrating with Polar Coordinates
Slicing Cold PizzaFirst, let's forget about calculus and use our knowledge of fractions to answer the following question.Sample ProblemWhat is the area of the shaded region?Answer.Think of the shad...
Volume
We know how to integrate our favorite flat foods to find their areas. Our next step is to learn how to integrate our favorite 3-D foods to find their volumes. In terms of the methods we'll lear...
Volume of Solids of Revolution
Solids of revolution aren't fruits thrown at tyrannical rulers in protest. A solid of revolution is a 3D object built by rotating an area around a predetermined center line called the axis of rotat...
Arc Length
We've prepared our fish by cutting it into flat rectangular portions and diced our vegetables into thin slices. We've even gone off on a tangent, playing with frisbees and toilet paper tubes. We're...
In the Real World
In this section we left the integrating to the calculators. That's practical, because calculators can integrate much more quickly and accurately than we can. Instead, we've been spending our time p...