Lösung 2.2:1a
Aus Online Mathematik Brückenkurs 2
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Version vom 10:20, 11. Mär. 2009
A substitution of variables is often carried out so as to transform a complicated integral to one that is less complicated which one can either directly calculate or continue to work with.
When we carry out a substitution of variables
- the integral must be rewritten in terms of the new variable
u ; - the element of integration,
dx , is replaced bydu , according to the formuladu=u ;(x)dx
- the limits of integration are for
x and must be changed to limits of integration for the variableu .
In this case, we will perform the change of variables (3x−1)4
u4
The relation between
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which means that
Furthermore, when 1−1=2
2−1=5
One usually writes the whole substitution of variables as
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Sometimes, we are more brief and hide the details,
![]() ![]() ![]() ![]() |
After the substitution of variables, we have a standard integral which is easy to compute.
In summary, the whole calculation is,
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