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

Lösung

\int_{0}^{1} (x^{2} + 2)^{2} d x

\frac{83}{15}

Dezimale

5.53333 \dots

Schritte zur Lösung

\int_{0}^{1} (x^{2} + 2)^{2} d x

Multipliziere aus

(x^{2} + 2)^{2} : x^{4} + 4 x^{2} + 4

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

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int_{0}^{1} x^{4} d x = \frac{1}{5}

\int_{0}^{1} 4 x^{2} d x = \frac{4}{3}

\int_{0}^{1} 4 d x = 4

= \frac{1}{5} + \frac{4}{3} + 4

Vereinfache

\frac{1}{5} + \frac{4}{3} + 4 : \frac{83}{15}

= \frac{83}{15}

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