Integralrechnung in der Analysis

Substitutionsregel und wichtige Stammfunktionen

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J_ Ravi

Set of flashcards Details

Flashcards	21
Language	Deutsch
Category	Maths
Level	University
Created / Updated	22.03.2014 / 14.02.2019
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Linearitätsregel

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∫ f(ax + b) dx = 1/a * F(ax + b) + c

1) Stammfunktion von f --> F
2) Copy (ax + b)
3) Multiplikation mit Korrekturfaktor --> Kehrwert von a

Spezialfall der Produktregel

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∫ f (x) * f ' (x) = 1/2 * (f(x))^2 + c

Quotientenregel

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∫ (f ' (x))/(f(x)) dx = ln(| f(x) |) + c

Substitutionsregel

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∫ f (g(x)) * g ' (x) dx = F(g(x)) + c

∫ f ' (g(x)) * g ' (x) dx = f(g(x)) + c

∫ (d/dx f(x)) dx

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f(x) + c

∫ x^a dx

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(1 / (a+1)) * x^a+1

(!)für alle 'a' ohne a = -1(!)

∫ K dx

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K * x + c

∫ x dx

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1/2 * x²

∫ √x dx

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2/3 * x^3/2+ c

∫ 1/√x dx

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2√x + c

∫ 1/x dx

ln(|x|) + c

∫ e^xdx

e^x + c

∫ a^x dx

( 1/ln(a) ) * a^x + c

∫ sin(x) dx

-cos(x) + c

∫ cos(x) dx

sin(x) + c

Produktregel (Partielle Integration)

∫ (f(x) * g'(x)) dx = f(x) * g(x) - ∫ (f'(x) * g(x)) dx

Signal: Auswirkung einer Spiegelung an t-Achse

s(t) -> -s(t)

a0 -> -a0; ak -> -ak; bk -> -bk; A0 -> -A0; phi -> phi + pi

Signal: Spiegelung an der Ordinatenachse

s(t) -> s(-t)

ak -> ak; bk -> -bk; Ak -> Ak; phi -> -phi

Signal: Streckung entlang der Ordinate (Streckungsfacktor F > 0)

s(t) -> F * s(t)

a0 -> F * a0; ak -> F * ak; bk -> F * bk; A0 -> F * A0; Ak -> F * Ak

Signal: Streckung entlang der t-Achse (Stauchung auf 1/F-Faches: F>0)

s(t) -> s(F * t)

w1 -> w1 * F

Signal: Verschiebung um eine Konstante c nach oben

s(t) -> s(t) + c

a0 -> a0 + c; A0 -> A0 + c

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Integralrechnung in der Analysis

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