integral from 0 to 2 of (x^2+3x-1)e^{2x}

Lösung

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

3 e^{4} + 1

Dezimale

164.79445 \dots

Schritte zur Lösung

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

Wende die partielle Integration an

= [\frac{1}{2} e^{2 x} (x^{2} + 3 x - 1) - \int e^{2 x} x + \frac{3}{2} e^{2 x} d x]_{0}^{2}

\int e^{2 x} x + \frac{3}{2} e^{2 x} d x = \frac{1}{2} e^{2 x} x + \frac{1}{2} e^{2 x}

= [\frac{1}{2} e^{2 x} (x^{2} + 3 x - 1) - (\frac{1}{2} e^{2 x} x + \frac{1}{2} e^{2 x})]_{0}^{2}

Multipliziere aus

\frac{1}{2} e^{2 x} (x^{2} + 3 x - 1) - (\frac{1}{2} e^{2 x} x + \frac{1}{2} e^{2 x}) : \frac{1}{2} e^{2 x} x^{2} + e^{2 x} x - e^{2 x}

= [\frac{1}{2} e^{2 x} x^{2} + e^{2 x} x - e^{2 x}]_{0}^{2}

Berechne die Grenzen:

3 e^{4} + 1

= 3 e^{4} + 1

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

\int_{\frac{π}{4}}^{\frac{π}{2}} 7 cot^{3} (x) d x

\int_{1.5}^{2} (2 - x) d x

\int_{0}^{2} 16 d x

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