integral from-1 to 0 of x/(sqrt(1-x^2))

Lösung

\int_{- 1}^{0} \frac{x}{1 - x ^{2}} d x

- 1

Schritte zur Lösung

\int_{- 1}^{0} \frac{x}{1 - x ^{2}} d x

Wende U-Substitution an

= \int_{0}^{1} - \frac{1}{2 u} d u

Entferne die Konstante:

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

= - \frac{1}{2} \cdot \int_{0}^{1} \frac{1}{u} d u

Wende die Potenzregel an

= - \frac{1}{2} [2 u^{\frac{1}{2}}]_{0}^{1}

Wende Radikal Regel an:

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

= - \frac{1}{2} [2 u]_{0}^{1}

Berechne die Grenzen:

2

= - \frac{1}{2} \cdot 2

Vereinfache

= - 1

\int_{0}^{2} 2 e^{x^{2} - 2 x} d x

\int_{0}^{\frac{π}{4}} t cos (2 t) d t

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