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Beliebt Rechnen >

integral from 0 to 1 of e^{sqrt(x)}

Lösung

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

Lösung

2

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{0}^{1} e^{u} \cdot 2 u d u

Entferne die Konstante:

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

= 2 \cdot \int_{0}^{1} e^{u} u d u

Wende die partielle Integration an

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

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

= 2 [e^{u} u - e^{u}]_{0}^{1}

Berechne die Grenzen:

1

= 2 \cdot 1

Vereinfache

= 2

Graph

Beliebte Beispiele

derivative of sqrt(x+a)

\frac{d}{d x} (x + a)

derivative of ln(x-y)

\frac{d}{d x} (ln (x - y))

derivative of 1/(\sqrt[9]{x})

\frac{d}{d x} (\frac{1}{9 x})

(\partial)/(\partial x)((x*y)/(x^2+y^2))

\frac{\partial}{\partial x} (\frac{x \cdot y}{x ^{2} + y ^{2}})

integral of x(sin(x)-cos(x^2))

\int x (sin (x) - cos (x^{2})) d x