integral from 0 to 1 of x^4-x^2

Lösung

\int_{0}^{1} x^{4} - x^{2} d x

- \frac{2}{15}

Dezimale

- 0.13333 \dots

Schritte zur Lösung

\int_{0}^{1} x^{4} - x^{2} 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} x^{2} d x

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

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

= \frac{1}{5} - \frac{1}{3}

Vereinfache

\frac{1}{5} - \frac{1}{3} : - \frac{2}{15}

= - \frac{2}{15}

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\int_{1}^{5} \frac{2}{x ^{2}} d x