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Beliebt Rechnen >

integral from 0 to 1 of θx^θ

Lösung

\int_{0}^{1} θ x^{θ} d x

Lösung

\frac{θ}{θ + 1}

Schritte zur Lösung

\int_{0}^{1} θ x^{θ} d x

Entferne die Konstante:

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

= θ \cdot \int_{0}^{1} x^{θ} d x

Wende die Potenzregel an

= θ [\frac{x ^{θ + 1}}{θ + 1}]_{0}^{1}

Berechne die Grenzen:

\frac{1}{θ + 1}

= θ \frac{1}{θ + 1}

Vereinfache

= \frac{θ}{θ + 1}

Beliebte Beispiele

integral from 0 to 1 of (x^3-x^2+1)

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

integral from 0 to x of 2x^2

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

integral from-6 to 6 of x

\int_{- 6}^{6} x d x

integral from x/2 to 1/2 of x^2e^{y^2}

\int_{\frac{x}{2}}^{\frac{1}{2}} x^{2} e^{y^{2}} d y

integral from 2 to 10 of x^3

\int_{2}^{10} x^{3} d x