Introduction to Integration (CIE IGCSE Additional Maths)

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

 

• • 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”