integral from 0 to 2 of 2/(sqrt(6-x^2))

Lösung

\int_{0}^{2} \frac{2}{6 - x ^{2}} d x

2 arcsin (\frac{2}{3})

Dezimale

1.91063 \dots

Schritte zur Lösung

\int_{0}^{2} \frac{2}{6 - x ^{2}} d x

Entferne die Konstante:

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

= 2 \cdot \int_{0}^{2} \frac{1}{6 - x ^{2}} d x

Trigonometrische Substitution anwenden

= 2 \cdot \int_{0}^{a r c s i n (\frac{2}{3})} 1 d u

Integral einer Konstanten :

\int a d x = a x

= 2 [1 \cdot u]_{0}^{a r c s i n (\frac{2}{3})}

Vereinfache

= 2 [u]_{0}^{a r c s i n (\frac{2}{3})}

Berechne die Grenzen:

arcsin (\frac{2}{3})

= 2 arcsin (\frac{2}{3})

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