integral from 0 to 1 of xe^x-x

Lösung

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

\frac{1}{2}

Dezimale

0.5

Schritte zur Lösung

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

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

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

= 1 - \frac{1}{2}

Vereinfache

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

= \frac{1}{2}

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

\int_{y}^{8 - y} \frac{3}{x ^{2} + y ^{2}} d y

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