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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
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)
Look out for questions that ask you to find an
indefinite integral in one part (so “ +c” needed), then in a later part use the same integral as a definite integral (where “ +c” is not needed).