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Beliebt Rechnen >

integral from 0 to 6 of e^t-e^{-t}

Lösung

\int_{0}^{6} e^{t} - e^{- t} d t

Lösung

\frac{e ^{12} + 1}{e ^{6}} - 2

+1

Dezimale

401.43127 \dots

Schritte zur Lösung

\int_{0}^{6} e^{t} - e^{- t} d t

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int_{0}^{6} 2 sinh (t) d t

Entferne die Konstante:

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

= 2 \cdot \int_{0}^{6} sinh (t) d t

Nutze das gemeinsame Integral :

\int sinh (t) d t = cosh (t)

= 2 [cosh (t)]_{0}^{6}

Berechne die Grenzen:

\frac{e ^{12} + 1}{2 e ^{6}} - 1

= 2 (\frac{e ^{12} + 1}{2 e ^{6}} - 1)

Vereinfache

= \frac{e ^{12} + 1}{e ^{6}} - 2

Graph

Beliebte Beispiele

integral from 0 to 6 of (x)

\int_{0}^{6} (x) d x

integral from-1 to 1 of x^{5/3}

\int_{- 1}^{1} x^{\frac{5}{3}} d x

integral from-1 to 0 of 3x^2

\int_{- 1}^{0} 3 x^{2} d x

integral from 5 to 7 of 1/x

\int_{5}^{7} \frac{1}{x} d x

integral from pi/6 to pi/4 of sec^2(x)

\int_{\frac{π}{6}}^{\frac{π}{4}} sec^{2} (x) d x