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6.1.3 Definite Integration

This document discusses definite integration, which is an alternative version of the fundamental theorem of calculus. It defines definite integration, explains how the constant of integration is handled differently than indefinite integration, provides steps for evaluating definite integrals, and includes an example problem.

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14 views4 pages

6.1.3 Definite Integration

This document discusses definite integration, which is an alternative version of the fundamental theorem of calculus. It defines definite integration, explains how the constant of integration is handled differently than indefinite integration, provides steps for evaluating definite integrals, and includes an example problem.

Uploaded by

King Howler
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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CIE A Level Maths: Pure 1

Revision Notes

6.1.3 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
⎛⎜ 1256 ⎞⎟
⎜ ⎟ of the integral)
⎝ 3 ⎠

Exam Tip
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).

Worked example
Find the value of

∫2 3x (x 2 − 2) dx
4

Start by expanding the brackets inside the integral

Integrate as usual (here it's a 'powers of ' integration)


Write the answer in square brackets with the integration limits
outside
Now substitute 4 into that function
And subtract from it the function with 2 substituted in

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