integral from 0 to 2 of x/(1+x^4)

Lösung

\int_{0}^{2} \frac{x}{1 + x ^{4}} d x

\frac{1}{2} arctan (4)

Dezimale

0.66290 \dots

Schritte zur Lösung

\int_{0}^{2} \frac{x}{1 + x ^{4}} d x

Berechne das unbestimmte Integral:

\int \frac{x}{1 + x ^{4}} d x = \frac{1}{2} arctan (x^{2}) + C

Berechne die Grenzen:

\int_{0}^{2} \frac{x}{1 + x ^{4}} d x = \frac{1}{2} arctan (4) - 0

= \frac{1}{2} arctan (4) - 0

Vereinfache

= \frac{1}{2} arctan (4)

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