Chapter 9

Integration

Chapter description
In this chapter, we discover what kinds of information we can find out if we do the reverse process to differentiating. This includes finding areas and also finding the equations of functions if we know their rates of change.
The chapter is split up into the following sections.

  1. Doing the opposite of differentiating
    1. What could this tell us?
    2. A physical interpretation of this process
    3. Finding the area under a curve
    4. What happens if the area we are finding is below the horizontal axis?
    5. What happens if we change the order of the limits?
    6. What is the integral of 1 over x?

  2. Techniques of integration
    1. Making use of what we already know
    2. Integration by substitution
    3. A selection of trig integrals with some hyperbolic cousins
    4. Integrals which use inverse trig and hyperbolic functions
    5. Using partial fractions in integration
    6. Integration by parts
    7. Finding rules for integrating functions like sinnx
    8. Using the t = tan (x/2) substitution

  3. Solving some more differential equations
    1. Solving equations where we can split up the variables
    2. Putting flesh on the bones -- some practical uses for differential equations
    3. A forwards look at some other kinds of differential equation, including ones which describe SHM
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