We'll discuss several integration technique that is definitely useful to know for exam or just out of curiosity.
@ TECHNIQUES COVERED (in order):
1. U-substitution
2. Partial Fraction
3. Trigonometric Substitution
4. Integration by Parts
Optional :
- Hyperbolic trigonometric integration
- Involving inverse trigonometric form
- Weierstrass Substitution
@ How to succeed in this course ?
Integration is the same as any other part of maths which you can improve by doing a lot of problems. Whether you're studying this on your own or at school, you're more than welcome to ask any questions (hint to questions) or concept that you are still unclear about. Discussion with others also highly encouraged.
@ PREREQUISITE KNOWLEDGE :
- Basic derivatives (literally basic) of these:
Polynomial, trigonometry, Natural logarithm, exponent (eg : 2^x)
- Comfortable with the ideas of:
trigonometric compound formula, Trigonometric identities, Natural logarithm properties, exponents, factorisation and expanding expressions
In some sessions I'll review some of the properties that I mentioned in "Comfortable with..". The more we delve into the courses the more all of these become off the top of our head.
@ Feedback
There will be a mini-exam after every techniques. As these techniques are foundations to each other we need to make sure we are really okay to moving on and not letting misunderstanding / confusion neglected.
There will be a real test after everything's been covered and some questionnaire
