Antiderivative: Difference between revisions
Appearance
Content deleted Content added
Changed (what I believe) is a mistake in the last example. |
Improved section. |
||
Line 12: | Line 12: | ||
To find the antiderivative of a simple equation <math>ax^n</math> |
To find the antiderivative of a simple equation <math>ax^n</math> |
||
* the power <math>n</math> |
* add 1 to the power <math>n</math>, so <math>ax^n</math> is now <math>ax^{n+1}</math> |
||
* divide all this by the new power, so it is now <math>\frac{ax^{n+1}}{n+1}</math> |
|||
* the whole equation should be divided by the new power |
|||
* and a constant <math>c</math> should be added |
* and a constant <math>c</math> should be added. |
||
This can be shown as: |
This can be shown as: |
||
Line 20: | Line 20: | ||
<math>\int ax^n\ dx = \frac{ax^{n+1}}{n+1}\ +\ c</math> |
<math>\int ax^n\ dx = \frac{ax^{n+1}}{n+1}\ +\ c</math> |
||
When there is many <math>x</math> terms, integrate each part on its own: |
|||
<math>\int 2x^6 - 5x^4\ dx = \frac{2x^7}{7} - \frac{5x^5}{5} + c = \frac{2}{7}x^7 - x^5 + c</math> |
<math>\int 2x^6 - 5x^4\ dx = \frac{2x^7}{7} - \frac{5x^5}{5} + c = \frac{2}{7}x^7 - x^5 + c</math> |
||
'''(This only works if the parts are being added or taken away.)''' |
|||
== Examples == |
== Examples == |
Revision as of 15:50, 14 June 2008
![]() | The English used in this Difficult subject to explain simply. may not be easy for everybody to understand. |
Antidifferentiation (or indefinite integration) is a part of mathematics. It is the opposite of differentiation. It is integrating with no limits. The answer is an equation.
It is written as
- with the integral sign that has no limits
- the equation you are integrating
- and the which means "with respect to ", which does not mean anything with simple integration.
Finding a simple antiderivative
To find the antiderivative of a simple equation
- add 1 to the power , so is now
- divide all this by the new power, so it is now
- and a constant should be added.
This can be shown as:
When there is many terms, integrate each part on its own:
(This only works if the parts are being added or taken away.)
Examples
Changing fractions and roots into powers makes it easier: