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Beliebt Rechnen >

integral from-1 to 1 of (x^2)/(1+x^6)

Lösung

\int_{- 1}^{1} \frac{x ^{2}}{1 + x ^{6}} d x

Lösung

\frac{π}{6}

+1

Dezimale

0.52359 \dots

Schritte zur Lösung

\int_{- 1}^{1} \frac{x ^{2}}{1 + x ^{6}} d x

Berechne das unbestimmte Integral:

\int \frac{x ^{2}}{1 + x ^{6}} d x = \frac{1}{3} arctan (x^{3}) + C

Berechne die Grenzen:

\int_{- 1}^{1} \frac{x ^{2}}{1 + x ^{6}} d x = \frac{π}{12} - (- \frac{π}{12})

= \frac{π}{12} - (- \frac{π}{12})

Vereinfache

= \frac{π}{6}

Graph

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