de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral from 0 to 9 of pie^{-(2x)/9}

Lösung

\int_{0}^{9} π e^{- \frac{2 x}{9}} d x

Lösung

\frac{9 π ( e ^{2} - 1 )}{2 e ^{2}}

+1

Dezimale

12.22390 \dots

Schritte zur Lösung

\int_{0}^{9} π e^{- \frac{2 x}{9}} d x

Entferne die Konstante:

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

= π \cdot \int_{0}^{9} e^{- \frac{2 x}{9}} d x

Wende U-Substitution an

= π \cdot \int_{0}^{- 2} - \frac{9}{2} e^{u} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= π (- \int_{- 2}^{0} - \frac{9}{2} e^{u} d u)

Entferne die Konstante:

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

= π (- (- \frac{9}{2} \cdot \int_{- 2}^{0} e^{u} d u))

Nutze das gemeinsame Integral :

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

= π (- (- \frac{9}{2} [e^{u}]_{- 2}^{0}))

Vereinfache

= π \frac{9}{2} [e^{u}]_{- 2}^{0}

Berechne die Grenzen:

1 - \frac{1}{e ^{2}}

= π \frac{9}{2} (1 - \frac{1}{e ^{2}})

Vereinfache

= \frac{9 π ( e ^{2} - 1 )}{2 e ^{2}}

Graph

Beliebte Beispiele

integral of x^3sqrt(x^2+11)

\int x^{3} x^{2} + 11 d x

y^{''}+4y^'+5y=e^x

y^{^{''}} + 4 y^{^{'}} + 5 y = e^{x}

integral from 0 to 5 of 1/(25-x^2)

\int_{0}^{5} \frac{1}{25 - x ^{2}} d x

limit as x approaches-1-of 9/(x^3-1)

x \to - 1 - lim (\frac{9}{x ^{3} - 1})

integral of 3/(sqrt(16-x^2))

\int \frac{3}{16 - x ^{2}} d x