integral from 0 to 1 of (x^4)^2-(x^7)^2

Lösung

\int_{0}^{1} (x^{4})^{2} - (x^{7})^{2} d x

\frac{2}{45}

Dezimale

0.04444 \dots

Schritte zur Lösung

\int_{0}^{1} (x^{4})^{2} - (x^{7})^{2} d x

Vereinfache

(x^{4})^{2} - (x^{7})^{2} : x^{8} - x^{14}

= \int_{0}^{1} x^{8} - x^{14} 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^{8} d x - \int_{0}^{1} x^{14} d x

\int_{0}^{1} x^{8} d x = \frac{1}{9}

\int_{0}^{1} x^{14} d x = \frac{1}{15}

= \frac{1}{9} - \frac{1}{15}

Vereinfache

\frac{1}{9} - \frac{1}{15} : \frac{2}{45}

= \frac{2}{45}

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