AQA A Level Maths: Pure復(fù)習(xí)筆記8.1.3 Definite Integration
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?