integral from 0 to 3 of (3x)^2-(x^2)^2

Lösung

\int_{0}^{3} (3 x)^{2} - (x^{2})^{2} d x

\frac{162}{5}

Dezimale

32.4

Schritte zur Lösung

\int_{0}^{3} (3 x)^{2} - (x^{2})^{2} d x

Vereinfache

(3 x)^{2} - (x^{2})^{2} : 9 x^{2} - x^{4}

= \int_{0}^{3} 9 x^{2} - x^{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}^{3} 9 x^{2} d x - \int_{0}^{3} x^{4} d x

\int_{0}^{3} 9 x^{2} d x = 81

\int_{0}^{3} x^{4} d x = \frac{243}{5}

= 81 - \frac{243}{5}

Vereinfache

81 - \frac{243}{5} : \frac{162}{5}

= \frac{162}{5}