integral from 0 to 1 of 2x^2-2x^3

Lösung

\int_{0}^{1} 2 x^{2} - 2 x^{3} d x

\frac{1}{6}

Dezimale

0.16666 \dots

Schritte zur Lösung

\int_{0}^{1} 2 x^{2} - 2 x^{3} 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} 2 x^{2} d x - \int_{0}^{1} 2 x^{3} d x

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

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

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

Vereinfache

\frac{2}{3} - \frac{1}{2} : \frac{1}{6}

= \frac{1}{6}

\int_{0}^{e x} t (t - π) e^{- t^{2}} d t

\int_{1}^{e} in x d x

\int_{0}^{1} e^{x} - x \cdot e^{x} d x

\int_{2}^{7} 2 x + 1 d x

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