Fundamental Theorem of Calculus (OCR A Level Maths A) : Revision Note

Fundamental Theorem of Calculus

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 “+c” (plus 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

Notation

• is the sign for integration

• 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”

• dx means integrate with respect to x, any other letter is treated like a number (ie like a constant)