integral from-1 to 2 of x^2e^{4x}

Lösung

\int_{- 1}^{2} x^{2} e^{4 x} d x

e^{8} - \frac{7 e ^{8}}{32} - \frac{13}{32 e ^{4}}

Dezimale

2328.86598 \dots

Schritte zur Lösung

\int_{- 1}^{2} x^{2} e^{4 x} d x

Wende die partielle Integration an

= [\frac{1}{4} e^{4 x} x^{2} - \int \frac{1}{2} e^{4 x} x d x]_{- 1}^{2}

\int \frac{1}{2} e^{4 x} x d x = \frac{1}{32} (4 e^{4 x} x - e^{4 x})

= [\frac{1}{4} e^{4 x} x^{2} - \frac{1}{32} (4 e^{4 x} x - e^{4 x})]_{- 1}^{2}

Berechne die Grenzen:

e^{8} - \frac{7 e ^{8}}{32} - \frac{13}{32 e ^{4}}

= e^{8} - \frac{7 e ^{8}}{32} - \frac{13}{32 e ^{4}}

\int_{- 4}^{1} (2 x + 4) d x

\int_{0}^{2} (3 t - 1)^{54} d t

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

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

\int_{0}^{x} (1 + t) d t