integral from 0 to 1 of 1/(sqrt(25-x^2))

Lösung

\int_{0}^{1} \frac{1}{25 - x ^{2}} d x

arcsin (\frac{1}{5})

Dezimale

0.20135 \dots

Schritte zur Lösung

\int_{0}^{1} \frac{1}{25 - x ^{2}} d x

Trigonometrische Substitution anwenden

= \int_{0}^{a r c s i n (\frac{1}{5})} 1 d u

Integral einer Konstanten :

\int a d x = a x

= [1 \cdot u]_{0}^{a r c s i n (\frac{1}{5})}

Vereinfache

= [u]_{0}^{a r c s i n (\frac{1}{5})}

Berechne die Grenzen:

arcsin (\frac{1}{5})

= arcsin (\frac{1}{5})

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