February 2015
Intermediate to advanced
392 pages
17h 52m
German
Content preview from Mathematik für Wirtschaftswissenschaftler, 2nd Edition
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9.4. Uneigentliche Integrale 271
kann jedoch der Integrand vereinfacht werden, wobei in den neuen Integrationsgrenzen
jetzt die Parameter auftreten:
6 ^
1 r (.-„)=• 1 ft' ,
— / e
-
dx
- —= / e
-
T
dt.
9.32
aV2ñ J Λ/2τγ J
9.4 Uneigentliche Integrale
9.4.1 (Uneigentliches Integral) Ist die Funktion f(x) für alle χ rechts bzw. links
κ
von einem Punkt a stetig, so kann das Verhalten des bestimmten Integrals f f(x) dx
bzw. f f(x) dx für große bzw. kleine Werte von Κ untersucht werden. Falls die Grenz-
te
werte für Κ
—>
oo bzw. Κ —oo existieren, so heißen diese uneigentliche Integrale
der Funktion f. Bezeichnungen:
Κ oo a a
^lim J f(x)
dx
= J f(x)dx, ...
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