integral from-1 to 1 of 2/(sqrt(4-x^2))

Lösung

\int_{- 1}^{1} \frac{2}{4 - x ^{2}} d x

\frac{2 π}{3}

Dezimale

2.09439 \dots

Schritte zur Lösung

\int_{- 1}^{1} \frac{2}{4 - x ^{2}} d x

Entferne die Konstante:

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

= 2 \cdot \int_{- 1}^{1} \frac{1}{4 - x ^{2}} d x

Trigonometrische Substitution anwenden

= 2 \cdot \int_{- \frac{π}{6}}^{\frac{π}{6}} 1 d u

Integral einer Konstanten :

\int a d x = a x

= 2 [1 \cdot u]_{- \frac{π}{6}}^{\frac{π}{6}}

Vereinfache

= 2 [u]_{- \frac{π}{6}}^{\frac{π}{6}}

Berechne die Grenzen:

\frac{π}{3}

= 2 \cdot \frac{π}{3}

Vereinfache

= \frac{2 π}{3}

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