6.1.3 Definite Integration

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)

Exam Tip

Worked Example