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

Lösung

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

- \frac{13}{12}

Dezimale

- 1.08333 \dots

Schritte zur Lösung

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

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

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

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

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

Vereinfache

\frac{1}{4} - \frac{1}{3} - 1 : - \frac{13}{12}

= - \frac{13}{12}

\int_{- 3}^{4} 25 - x^{2} d x

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

\int_{1}^{5} 3 x^{2} + 7 x d x

\int_{1}^{2} t e^{- s t} d t

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