integral from 1 to 8 of xe^{x^2}

Lösung

\int_{1}^{8} x e^{x^{2}} d x

\frac{e ^{64} - e}{2}

Dezimale

3.11757 E 27

Schritte zur Lösung

\int_{1}^{8} x e^{x^{2}} d x

Wende U-Substitution an

= \int_{1}^{64} \frac{e ^{u}}{2} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{1}^{64} e^{u} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{2} [e^{u}]_{1}^{64}

Berechne die Grenzen:

e^{64} - e

= \frac{1}{2} (e^{64} - e)

Vereinfache

= \frac{e ^{64} - e}{2}

\int_{0}^{1} f (1 - x) d x

\int_{0}^{1} e^{x} + x^{e} d x

\int_{0}^{2} \frac{2}{x ^{3}} d x

\int_{- 2}^{2} (- 5 x^{2} - 4 x)^{3} d x

\int_{0}^{\infty} 9 e^{- 3 x} d x