8D - volume of revolution
Objective: to visualize how the area bounded by a curve can be rotated around/about either the x or y axis and evaluate it's volume using integration.
Posts
7h- Further techniques and miscellaneous exercises
in this exercise, you will get to revise on the different integration techniques learned in this chapter. The example below is similar to the problems you've done in Maths methods ( Exercise 11H ). This is where you first derive a function, then use the dy/dx to antidiff one of the terms in the derivative function.
7G- Using partial fractions with integration
objectives: you need to be familiar with the partial fractions techniques. There are 4 cases to consider: when the denominator consists of single factors (x+a)(x+b) when the denominator consists of a single factor (x+a) and a repeated factor, usually a perfect square (x+b)^2. This gives you three partial fractions when the denominator consists of a factor (x+a) and an irreducible quadratic expression. When you have P(x)/Q(x); division of two polynomials. It is wise to apply long division ( click here to revise on long division ) AND THEN apply partial fractions to simplify them. Question 2b) three partial fractions
7F- Further substitution
7F - Further substitution You will be able to integrate expressions by substitution. Knowledge of trigonometry identities is required.