integral from 0 to 1 of 10xe^x

Lösung

\int_{0}^{1} 10 x e^{x} d x

10

Schritte zur Lösung

\int_{0}^{1} 10 x e^{x} d x

Entferne die Konstante:

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

= 10 \cdot \int_{0}^{1} x e^{x} d x

Wende die partielle Integration an

= 10 [e^{x} x - \int e^{x} d x]_{0}^{1}

\int e^{x} d x = e^{x}

= 10 [e^{x} x - e^{x}]_{0}^{1}

Berechne die Grenzen:

1

= 10 \cdot 1

Vereinfache

= 10

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

\int_{0}^{s i n (x)} ln (t^{3} + 1) d t

\int_{2}^{\infty} x e^{- \frac{x}{2}} d x

\int_{0}^{π} 1 - sin (x) d x

\int_{0}^{1} a x d x