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Beliebt Rechnen >

integral from 0 to 1 of 8e^{2sqrt(x)}

Lösung

\int_{0}^{1} 8 e^{2 x} d x

Lösung

4 (e^{2} + 1)

+1

Dezimale

33.55622 \dots

Schritte zur Lösung

\int_{0}^{1} 8 e^{2 x} d x

Entferne die Konstante:

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

= 8 \cdot \int_{0}^{1} e^{2 x} d x

Wende U-Substitution an

= 8 \cdot \int_{0}^{2} \frac{e ^{u} u}{2} d u

Entferne die Konstante:

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

= 8 \cdot \frac{1}{2} \cdot \int_{0}^{2} e^{u} u d u

Wende die partielle Integration an

= 8 \cdot \frac{1}{2} [e^{u} u - \int e^{u} d u]_{0}^{2}

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

= 8 \cdot \frac{1}{2} [e^{u} u - e^{u}]_{0}^{2}

Vereinfache

8 \cdot \frac{1}{2} [e^{u} u - e^{u}]_{0}^{2} : 4 [e^{u} u - e^{u}]_{0}^{2}

= 4 [e^{u} u - e^{u}]_{0}^{2}

Berechne die Grenzen:

e^{2} + 1

= 4 (e^{2} + 1)

Graph

Beliebte Beispiele

derivative 2e^x+8/(\sqrt[3]{x)}

d er i v a t i v e 2 e^{x} + \frac{8}{3 x}

derivative of ln(x^2e^{-x})

\frac{d}{d x} (ln (x^{2} e^{- x}))

steigung xy-2y^2=5,(11,5)

s l o p e x y - 2 y^{2} = 5, (11, 5)

integral from 1 to 2 of 9/(x^3+4x)

\int_{1}^{2} \frac{9}{x ^{3} + 4 x} d x

derivative of 5/2 x^2

\frac{d}{d x} (\frac{5}{2} x^{2})