integral from-1 to 1 of (20-12x)^{-1}

Lösung

\int_{- 1}^{1} (20 - 12 x)^{- 1} d x

\frac{1}{6} ln (2)

Dezimale

0.11552 \dots

Schritte zur Lösung

\int_{- 1}^{1} (20 - 12 x)^{- 1} d x

Wende Exponentenregel an:

a^{- 1} = \frac{1}{a}

= \int_{- 1}^{1} \frac{1}{20 - 12 x} d x

Wende U-Substitution an

= \int_{32}^{8} - \frac{1}{12 u} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{8}^{32} - \frac{1}{12 u} d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - (- \frac{1}{12} \cdot \int_{8}^{32} \frac{1}{u} d u)

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= - (- \frac{1}{12} [ln ∣ u ∣]_{8}^{32})

Vereinfache

= \frac{1}{12} [ln ∣ u ∣]_{8}^{32}

Berechne die Grenzen:

2 ln (2)

= \frac{1}{12} \cdot 2 ln (2)

Vereinfache

= \frac{1}{6} ln (2)

\int \frac{( sin ( 2 x ) )}{e ^{x}} d x

e x p an d x (4 - x)^{3}

d er i v a t i v e y = \frac{4}{x} + x + 0.5 - 5 x

t \to 0 lim (\frac{sin ^{2} ( 3 t )}{t})

\frac{\partial}{\partial y} (\frac{1}{x ^{2} + y ^{2} + z ^{2}})