IB DP Maths: AI HL复习笔记5.3.2 Introduction to Integration
Introduction to Integration
What is integration?
- Integration is the opposite to differentiation
- Integration is referred to as antidifferentiation
- The result of integration is referred to as the antiderivative
- Integration is the process of finding the expression of a function (antiderivative) from an expression of the derivative (gradient function)
What is the notation for integration?
- An integral is normally written in the form
What is the constant of integration?
Integrating Powers of x
How do I integrate powers of x?
What might I be asked to do once I’ve found the anti-derivative (integrated)?
The area under a curve can be found using integration
Exam Tip
- You can speed up the process of integration in the exam by committing the pattern of basic integration to memory
- In general you can think of it as 'raising the power by one and dividing by the new power'
- Practice this lots before your exam so that it comes quickly and naturally when doing more complicated integration questions
Worked Example
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