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Beliebt Rechnen >

integral from-1 to 1 of 4/(3e^{3x)}

Lösung

\int_{- 1}^{1} \frac{4}{3 e ^{3 x}} d x

Lösung

\frac{4 ( e ^{6} - 1 )}{9 e ^{3}}

+1

Dezimale

8.90477 \dots

Schritte zur Lösung

\int_{- 1}^{1} \frac{4}{3 e ^{3 x}} d x

Entferne die Konstante:

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

= \frac{4}{3} \cdot \int_{- 1}^{1} \frac{1}{e ^{3 x}} d x

Wende Exponentenregel an:

\frac{1}{a ^{b}} = a^{- b}

\frac{1}{e ^{3 x}} = e^{- 3 x}

= \frac{4}{3} \cdot \int_{- 1}^{1} e^{- 3 x} d x

Wende U-Substitution an

= \frac{4}{3} \cdot \int_{3}^{- 3} - \frac{1}{3} e^{u} d u

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

= \frac{4}{3} (- \int_{- 3}^{3} - \frac{1}{3} e^{u} d u)

Entferne die Konstante:

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

= \frac{4}{3} (- (- \frac{1}{3} \cdot \int_{- 3}^{3} e^{u} d u))

Nutze das gemeinsame Integral :

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

= \frac{4}{3} (- (- \frac{1}{3} [e^{u}]_{- 3}^{3}))

Vereinfache

\frac{4}{3} (- (- \frac{1}{3} [e^{u}]_{- 3}^{3})) : \frac{4}{9} [e^{u}]_{- 3}^{3}

= \frac{4}{9} [e^{u}]_{- 3}^{3}

Berechne die Grenzen:

e^{3} - \frac{1}{e ^{3}}

= \frac{4}{9} (e^{3} - \frac{1}{e ^{3}})

Vereinfache

= \frac{4 ( e ^{6} - 1 )}{9 e ^{3}}

Graph

Beliebte Beispiele

integral from-9 to 6 of (1-x)

\int_{- 9}^{6} (1 - x) d x

integral from pi/2 to pi of 1/2 e^{-x/4}

\int_{\frac{π}{2}}^{π} \frac{1}{2} e^{- \frac{x}{4}} d x

integral from-1 to 1 of x(x+1)(x-1)

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

integral from 0 to 3 of pi(x^3)^2

\int_{0}^{3} π (x^{3})^{2} d x

integral from 1 to e^2 of 5/x

\int_{1}^{e^{2}} \frac{5}{x} d x