integral from-1 to 2 of e^{5x-4}

Lösung

\int_{- 1}^{2} e^{5 x - 4} d x

\frac{e ^{15} - 1}{5 e ^{9}}

Dezimale

80.68573 \dots

Schritte zur Lösung

\int_{- 1}^{2} e^{5 x - 4} d x

Wende U-Substitution an

= \int_{- 9}^{6} e^{u} \frac{1}{5} d u

Entferne die Konstante:

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

= \frac{1}{5} \cdot \int_{- 9}^{6} e^{u} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{5} [e^{u}]_{- 9}^{6}

Berechne die Grenzen:

e^{6} - \frac{1}{e ^{9}}

= \frac{1}{5} (e^{6} - \frac{1}{e ^{9}})

Vereinfache

= \frac{e ^{15} - 1}{5 e ^{9}}

\int_{0}^{1} e^{- \frac{( x - 0.5 )}{2}} d x

\int_{1}^{4} (x^{2} - 4 x + 9) d x

\int_{0}^{\infty} e^{t - s t} d t

\int_{1}^{2} \frac{arccsc ( x )}{6} d x

\int_{0}^{1} 9 x^{8} (4 - x^{9}) d x