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

Lösung

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

\frac{17}{15}

Dezimale

1.13333 \dots

Schritte zur Lösung

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

Multipliziere aus

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

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

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

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

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

Vereinfache

\frac{4}{3} - \frac{1}{5} : \frac{17}{15}

= \frac{17}{15}