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Introduction to Integration (Cambridge O Level Additional Maths)
Revision Note
Introduction to Integration
What is integration?
- Integration is the opposite to differentiation
- Integration is the process of finding the expression of a function from an expression of the derivative (gradient function)
What is the fundamental theorem of calculus?
- The Fundamental Theorem of Calculus states that integration is the inverse process of differentiation
- This form of the Theorem relates to Indefinite Integration
- An alternative version of the Fundamental Theorem of Calculus involves Definite Integration
What is the constant of integration (+c)?
- When differentiating y, constant terms ‘disappear’
- for constants y = c,
- graphs of constants are horizontal lines and so have gradient of 0
- Integrating , to get y, cannot determine the constant
- To acknowledge this constant, “+ c” is used
- c is called the constant of integration
What is the notation for integration?
- An integral is normally written in the form
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- the large operator means “integrate”
- “” indicates which variable to integrate with respect to
- is the function to be integrated
- If it has more than one term the function to be integrated (called the integrand) should be in brackets
- “Integrate” -– “all of (…)” -– “with respect to x”
Worked example
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