integral from 0 to 1 of e^xsqrt(1-x)

Lösung

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

1.03007 \dots

Schritte zur Lösung

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

Wende die partielle Integration an

= [e^{x} 1 - x - \int - \frac{e ^{x}}{2 1 - x} d x]_{0}^{1}

\int - \frac{e ^{x}}{2 1 - x} d x = \frac{e π}{2} erf (1 - x)

= [e^{x} 1 - x - \frac{e π}{2} erf (1 - x)]_{0}^{1}

Berechne die Grenzen:

1.03007 \dots

= 1.03007 \dots

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

\int_{0}^{y} \frac{1}{y} d y

\int_{0}^{3} x^{3} 81 - x^{4} d x

\int_{0}^{1} arccos (x) d x

\int_{1}^{2} \frac{x ^{2} + 2 x + 4}{x} d x