integral from 0 to t of 5/(sqrt(1-x^2))

Lösung

\int_{0}^{t} \frac{5}{1 - x ^{2}} d x

5 arcsin (t)

Schritte zur Lösung

\int_{0}^{t} \frac{5}{1 - x ^{2}} d x

Entferne die Konstante:

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

= 5 \cdot \int_{0}^{t} \frac{1}{1 - x ^{2}} d x

Nutze das gemeinsame Integral :

\int \frac{1}{1 - x ^{2}} d x = arcsin (x)

= 5 [arcsin (x)]_{0}^{t}

Berechne die Grenzen:

arcsin (t)

= 5 arcsin (t)

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