411 REFERENCE · Wikibooks
Engineering Handbook/Mathematics/Integral
Reference material by Wikibooks contributors. This retains its source identity and is not 411 news reporting.
Integral
Indefinite Integral
{| class="wikitable" width=90% style="text-align:center; margin: 1em auto 1em auto"
!colspan=3 style="font-size:1.2em"|Table of Properties of Integrals
|-
!width=20%|
!width=50%|Rule
!Conditions
|-
|height=55| 1
|
|
|-
|height=55| 2 Homogeniety
|
|
|-
|height=55| 3 Associativity
|
|
|-
|height=55| 4 Integration by Parts
|
|
|-
|height=55| 4 General Integration by Parts
|
|
|-
|height=55| 5
|
|
|-
|height=55| 6 Substitution Rule
|
|
|-
|height=55| 7
|
|
|-
|height=55| 8
|
|
|-
|height=55| 9
|
|
|-
|height=55| 10
|
|
|-
!colspan=3|
|-
!style="background:#ebf0f7;; font-size:1.2em"| Notes:
|colspan=2 style="text-align:left"|
f, g, h are functions of x
a, n are constants.
The constant of integration, C has been omitted from this table. It should be included in the working of the equation if applicable.
|-
|colspan = 13 style="text-align:right"|:Engineering_Tables/Properties_of_Integrals
|}
{| class="wikitable" width=90% style="text-align:center; margin: 1em auto 1em auto"
!width=6%|
!width=32%|Integral
!width=32%|Value
!width=22%|Remarks
|-
| 1
|
|||
|-
| 2
|
|
|
|-
| 3
|
|||
|-
| 4
|
|||
|-
| 5
|
|||
|-
| 6
|
|||
|-
| 7
|
|||
|-
| 8
|
|||
|-
| 9
|
|||
|-
| 10
|
|||
|-
| 11
|
|||
|-
| 12
|
|||
|-
| 13
|
|||
|-
| 14
|
|||
|-
| 15
|
|||
|-
| 16
|
|||
|-
| 17
|
|||
|-
| 18
|
|||
|-
| 19
|
|||
|-
| 20
|
|||
|-
| 21
|
|||
|-
| 22
|
|||
|-
| 23
|
|||
|-
| 24
|
|||
|-
| 25
|
|||
|-
| 26
|
|||
|-
| 27
|
|||
|-
| 28
|
|||
|-
| 29
|
|||
|-
| 30
|
|||
|-
| 31
|
|||
|-
| 32
|
|||
|}
Definite Integral
200px
Furthermore, for every x in the interval (a, b),
References
Integral