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

Lösung

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

\frac{e ^{6} - 1}{4 e}

Dezimale

37.01131 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{- 1}^{5} \frac{e ^{u}}{4} d u

Entferne die Konstante:

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

= \frac{1}{4} \cdot \int_{- 1}^{5} e^{u} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{4} [e^{u}]_{- 1}^{5}

Berechne die Grenzen:

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

= \frac{1}{4} (e^{5} - \frac{1}{e})

Vereinfache

= \frac{e ^{6} - 1}{4 e}

\int_{0}^{π} 10 t sin (3 t) d t

x \to \infty lim (\frac{x \cdot ( x + 1 ) ^{x + 1}}{( x + 1 ) ^{x + 2}})

\int (sin (x))^{2} (cos (x))^{2} d x

s l o p e in t erce pt (2005, 54), (2010, 58)

\int u^{2} + 1 d u