integral from 2 to 4 of xe^{x^2}

Lösung

\int_{2}^{4} x e^{x^{2}} d x

\frac{e ^{16} - e ^{4}}{2}

Dezimale

4443027.96117 \dots

Schritte zur Lösung

\int_{2}^{4} x e^{x^{2}} d x

Wende U-Substitution an

= \int_{4}^{16} \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}^{16} e^{u} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{2} [e^{u}]_{4}^{16}

Berechne die Grenzen:

e^{16} - e^{4}

= \frac{1}{2} (e^{16} - e^{4})

Vereinfache

= \frac{e ^{16} - e ^{4}}{2}

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

\int_{0}^{1} \frac{2 x}{( x ^{2} - 3 ) ^{3}} d x

\int_{0}^{3} 2 x (x - 4) d x

\int_{4}^{\frac{1}{x}} arctan (5 t) d t

\int_{- 2}^{2} 9 - x^{2} d x