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Beliebt Rechnen >

integral from 1 to 16 of e^{sqrt(x)}

Lösung

\int_{1}^{16} e^{x} d x

Lösung

6 e^{4}

+1

Dezimale

327.58890 \dots

Schritte zur Lösung

\int_{1}^{16} e^{x} d x

Wende U-Substitution an

= \int_{1}^{4} 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_{1}^{4} e^{u} u d u

Wende die partielle Integration an

= 2 [e^{u} u - \int e^{u} d u]_{1}^{4}

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

= 2 [e^{u} u - e^{u}]_{1}^{4}

Berechne die Grenzen:

3 e^{4}

= 2 \cdot 3 e^{4}

Vereinfache

= 6 e^{4}

Graph

Beliebte Beispiele

y^{''}+4y^'+13y=3cos(2x)

y^{^{''}} + 4 y^{^{'}} + 13 y = 3 cos (2 x)

integral of 1/(y^5)

\int \frac{1}{y ^{5}} d y

y^{''}-y=0,y(0)=0,y(1)=1

y^{^{''}} - y = 0, y (0) = 0, y (1) = 1

integral of (e^{1/x})/(x^3)

\int \frac{e ^{\frac{1}{x}}}{x ^{3}} d x

limit as x approaches-1 of-12x^3

x \to - 1 lim (- 12 x^{3})