integral from 0 to 2 of 8x^2e^{2x}

Lösung

\int_{0}^{2} 8 x^{2} e^{2 x} d x

10 e^{4} - 2

Dezimale

543.98150 \dots

Schritte zur Lösung

\int_{0}^{2} 8 x^{2} e^{2 x} d x

Entferne die Konstante:

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

= 8 \cdot \int_{0}^{2} x^{2} e^{2 x} d x

Wende die partielle Integration an

= 8 [\frac{1}{2} e^{2 x} x^{2} - \int e^{2 x} x d x]_{0}^{2}

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

= 8 [\frac{1}{2} e^{2 x} x^{2} - \frac{1}{4} (e^{2 x} \cdot 2 x - e^{2 x})]_{0}^{2}

Berechne die Grenzen:

2 e^{4} - \frac{3 e ^{4}}{4} - \frac{1}{4}

= 8 (2 e^{4} - \frac{3 e ^{4}}{4} - \frac{1}{4})

Vereinfache

= 10 e^{4} - 2

\int_{0}^{l n (2)} 2 e^{2 x} d x

\int_{0}^{\frac{1}{2}} 1 + 4 x^{2} d x

\int_{9}^{16} (- x^{- \frac{1}{2}} + 5) d x

\int_{x}^{1} x y d y

\int_{0}^{y^{2} - 9 x^{2}} z d z