integral from 0 to 3 of xe^{4x}

Lösung

\int_{0}^{3} x e^{4 x} d x

\frac{11 e ^{12} + 1}{16}

Dezimale

111893.98160 \dots

Schritte zur Lösung

\int_{0}^{3} x e^{4 x} d x

Wende U-Substitution an

= \int_{0}^{12} \frac{e ^{u} u}{16} d u

Entferne die Konstante:

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

= \frac{1}{16} \cdot \int_{0}^{12} e^{u} u d u

Wende die partielle Integration an

= \frac{1}{16} [e^{u} u - \int e^{u} d u]_{0}^{12}

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

= \frac{1}{16} [e^{u} u - e^{u}]_{0}^{12}

Berechne die Grenzen:

11 e^{12} + 1

= \frac{1}{16} (11 e^{12} + 1)

Vereinfache

= \frac{11 e ^{12} + 1}{16}

d er i v a t i v e 3 sin (t)

x \to 0 lim (\frac{3 x}{x})

t an g e n t f (x) = \frac{2}{x}, (- 6, - \frac{1}{3})

\frac{d y}{d x} = 4 y^{3}

(2 x y + y) d x + (x^{2} - x) d y = 0