integral from 0 to 5 of 1/(1+x^2+y^2)

Lösung

\int_{0}^{5} \frac{1}{1 + x ^{2} + y ^{2}} d z

\frac{5}{x ^{2} + y ^{2} + 1}

Schritte zur Lösung

\int_{0}^{5} \frac{1}{1 + x ^{2} + y ^{2}} d z

Integral einer Konstanten :

\int a d x = a x

= [\frac{1}{1 + x ^{2} + y ^{2}} z]_{0}^{5}

Multipliziere

\frac{1}{1 + x ^{2} + y ^{2}} z : \frac{z}{1 + x ^{2} + y ^{2}}

= [\frac{z}{1 + x ^{2} + y ^{2}}]_{0}^{5}

Berechne die Grenzen:

\frac{5}{x ^{2} + y ^{2} + 1}

= \frac{5}{x ^{2} + y ^{2} + 1}

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