integral from-1 to 3 of xe^{x^2}

Lösung

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

\frac{e ^{9} - e}{2}

Dezimale

4050.18282 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{1}^{9} \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}^{9} e^{u} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{2} [e^{u}]_{1}^{9}

Berechne die Grenzen:

e^{9} - e

= \frac{1}{2} (e^{9} - e)

Vereinfache

= \frac{e ^{9} - e}{2}

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

\int_{1}^{2} (7 x^{2} - 57 x + 8) d x

\int_{0}^{1} \frac{1}{1 + 8 x} d x

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

\int_{3}^{5} \frac{5}{( 2 x + 1 ) ( x - 2 )} d x