Definite Integration (Cambridge (CIE) AS Maths: Pure 1): Revision Note

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)

Why is there no constant of integration in definite 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 the value of 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

How do I find a definite integral on my 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 $\left(\frac{1256}{3}\right)$ of the integral)