integral from 0 to 1 of x^2e^{2x}

Lösung

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

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

Dezimale

1.59726 \dots

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Berechne die Grenzen:

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

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

Vereinfache

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

\frac{d}{d x} (2 x y)

d er i v a t i v e 10 x - 3 x^{2}

t an g e n t f (x) = 3 x^{2} - 5 x + 2, at x = - 1

\int_{0}^{2 π} e^{i (θ - x)} d x

\int \frac{4 x ^{2}}{4 x - x ^{2}} d x