MA1102 Calculus Tutorial 10

Topics Covered:

Inverse trigonometric functions. Derivative of inverse trigonometric functions. More integral formulae. Integration of powers of sine or cosine. Integration by parts. Integration by trigonometric substitution. Integration by partial fractions. L' Hôpital's rule. (Application to calculation of limits). Taylor's Theorem.

Textbook: Chapter 11, Chapter 12, 12.1,12.2,12.4,12.5, Chapter 13, 13.1,13.2, 13.4

The trigonometric functions needed to be redefined in a way that its inverse exists. Strictly speaking we choose the appropriate domain so that each trigonometric function is injective. Applying the differentiation of inverse trigonometric function gives us more integral formulae. Integration by parts has many application in many surprising places. Look for them when you can. L'Hôpital's rule gives an effective method of computing limits of certain "indeterminate forms". Taylor's theorem is an example of how generalisation takes shape, often not in an obvious way. Behind every mathematical statement, there is a story to be told. We hope that you can discover some of these stories and that your path to the milestones and landscape in mathematics must have some of your own stories and anecdotes.