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

Lösung

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

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

Dezimale

1.59726 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{0}^{2} \frac{e ^{u}}{4} d u

Entferne die Konstante:

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

= \frac{1}{4} \cdot \int_{0}^{2} e^{u} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{4} [e^{u}]_{0}^{2}

Berechne die Grenzen:

e^{2} - 1

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

Vereinfache

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

n = 1 \sum \infty p (1 - p)^{2 n}

\frac{d y}{d x} = \frac{y ^{2} + 1}{x ^{2} + 1}, y (0) = 1

\int \frac{3 x ^{7}}{4 + x ^{8}} d x

f (x) = 5 lo g_{10} (4 x^{2})

\frac{d}{d x} (sin^{4} (2 x) cos^{4} (3 x))