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

Lösung

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

\frac{e ^{64} - e ^{4}}{2}

Dezimale

3.11757 E 27

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{4}^{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_{4}^{64} e^{u} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{2} [e^{u}]_{4}^{64}

Berechne die Grenzen:

e^{64} - e^{4}

= \frac{1}{2} (e^{64} - e^{4})

Vereinfache

= \frac{e ^{64} - e ^{4}}{2}

\int_{0}^{0.2} 25 e^{- 5 x} d x

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

\int_{x^{2}}^{x^{4}} (t + t^{2})^{2} d t

\int_{- 1}^{3} (3 + 2 x - x^{2}) d x

\int_{0}^{9} 9 - y d y