What is definite integration?

• Definite?Integration?occurs in an alternative version of the Fundamental Theorem of Calculus
• This version of the Theorem is the one referred to by most AS/A level textbooks/websites

• a?and?b?are called limits
  • a?is the lower limit
  • b?is the upper limit
• f’(x)?is the?derivative?of?f(x)

What happened to c, the constant of integration?

• ?“+c” would appear in both?f(a)?and?f(b)
  • Since we then calculate?f(b)?–?f(a)?they cancel each other out
  • There would be a “+c” from?f(b)?and a?–“+c” from?f(a)
• So “+c” is not included with definite integration

How do I find a definite integral?

• STEP 1: If not given a name, call the integral
  • This saves you having to rewrite the whole integral every time!
• STEP 2:? If necessary rewrite the integral into a more easily?integrable?form
  • Not all functions can be integrated directly
• STEP 3:? Integrate without applying the limits
  • Notation: use square brackets [ ] with limits placed after the end bracket
• STEP 4:? Substitute the limits into the function and calculate the answer

Using a calculator

• Advanced scientific calculators can work out the values of definite integrals
• The button will look similar to:

• ?(Note how the calculator did not return the exact value ?of the integral)