Differentialrechnung

From SkyWiki

(Difference between revisions)
Jump to: navigation, search
(Integrationsregeln)
(Integrationsregeln)
Line 106: Line 106:
<math>\int_a^x f(t) dt = F(x)|_a^x = F(x) - F(a)\qquad</math> unbestimmtes Integral
<math>\int_a^x f(t) dt = F(x)|_a^x = F(x) - F(a)\qquad</math> unbestimmtes Integral
-
<math>\int f(x) dx = \int f[\varphi(t)] \dot\varphi(t) dt\qquad</math> Integration durch Substitution, <math>x=\varphi(t),\ dx=\dot\varphi(t)dt</math>
+
Integration durch Substitution:
 +
 
 +
<math>\int f(x) dx = \int f[\varphi(t)] \dot\varphi(t) dt\quad x=\varphi(t),\ dx=\dot\varphi(t)dt \quad</math> oder
 +
 
 +
<math>\int_a^b f(x)\,dx = \int_{g^{-1}(a)}^{g^{-1}(b)} f(g(t))g'(t)\,dt,\ x = g(t)</math>
partielle Integration:
partielle Integration:
-
<math>\int uv'\,dx = uv - \int vu'\,dx,\ u=u(x),\ v=v(x)\quad</math> oder <math>\int u\,dv = uv-\int v\,du\quad</math> oder
+
<math>\int uv'\,dx = uv - \int vu'\,dx,\ u=u(x),\ v=v(x) \quad</math> oder <math>\int u\,dv = uv-\int v\,du \quad</math> oder
<math>\int_a^b u(x) v'(x)\,dx = [u(x) v(x)]_a^b - \int_a^b v(x) u'(x)\,dx</math>
<math>\int_a^b u(x) v'(x)\,dx = [u(x) v(x)]_a^b - \int_a^b v(x) u'(x)\,dx</math>

Revision as of 09:55, 17 September 2008

Funktion MathImage Ableitung MathImage Integral MathImage
MathImage MathImage MathImage
MathImage MathImage MathImage
MathImage MathImage MathImage
MathImage MathImage MathImage
MathImage MathImage MathImage
MathImage MathImage MathImage
MathImage MathImage
MathImage MathImage
MathImage MathImage MathImage
MathImage MathImage MathImage
MathImage MathImage
MathImage MathImage
MathImage MathImage
MathImage MathImage
MathImage MathImage
MathImage MathImage
MathImage MathImage MathImage
MathImage MathImage MathImage
MathImage MathImage MathImage
MathImage MathImage MathImage
MathImage MathImage
MathImage MathImage
MathImage MathImage
MathImage MathImage

Integrationsregeln

MathImage

MathImage

MathImage

MathImage

MathImage

MathImage

MathImage

MathImage unbestimmtes Integral

Integration durch Substitution:

MathImage oder

MathImage

partielle Integration:

MathImage oder MathImage oder

MathImage

weitere Integrale

Funktion MathImage Integral MathImage
MathImage MathImage
MathImage MathImage
MathImage MathImage
MathImage MathImage
MathImage MathImage
MathImage MathImage
MathImage MathImage
MathImage MathImage
MathImage MathImage
MathImage MathImage
MathImage MathImage
MathImage MathImage
MathImage MathImage
MathImage MathImage
MathImage MathImage

Integralfunktionen

Integralsinus MathImage Eulersche Konstante MathImage
Integralcosinus MathImage
Exponentialintegral MathImage
Integrallogarithmus MathImage
Gaußsches Fehlerintegral MathImage
Personal tools