integral from 0 to 1 of x*2(1-x)

Lösung

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

\frac{1}{3}

Dezimale

0.33333 \dots

Schritte zur Lösung

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

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Multipliziere aus

x (1 - x) : x - x^{2}

= 2 \cdot \int_{0}^{1} x - 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

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

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

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

= 2 (\frac{1}{2} - \frac{1}{3})

Vereinfache

2 (\frac{1}{2} - \frac{1}{3}) : \frac{1}{3}

= \frac{1}{3}

\int_{- 2}^{2} x^{2} + x + 2 d x

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

\int_{5}^{7} ∣ f (3 x) ∣ d x

\int_{0}^{15} x d x

\int_{0}^{1} (x + 3) e^{2 x} d x