integral from 1 to x^3 of 1/(1+t^2)

Lösung

\int_{1}^{x^{3}} \frac{1}{1 + t ^{2}} d t

arctan (x^{3}) - \frac{π}{4}

Schritte zur Lösung

\int_{1}^{x^{3}} \frac{1}{1 + t ^{2}} d t

Nutze das gemeinsame Integral :

\int \frac{1}{1 + t ^{2}} d t = arctan (t)

= [arctan (t)]_{1}^{x^{3}}

Berechne die Grenzen:

arctan (x^{3}) - \frac{π}{4}

= arctan (x^{3}) - \frac{π}{4}

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