integral from 0 to 1 of 3te^{8t^2}

Lösung

\int_{0}^{1} 3 t e^{8 t^{2}} d t

\frac{3 ( e ^{8} - 1 )}{16}

Dezimale

558.74212 \dots

Schritte zur Lösung

\int_{0}^{1} 3 t e^{8 t^{2}} d t

Entferne die Konstante:

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

= 3 \cdot \int_{0}^{1} t e^{8 t^{2}} d t

Wende U-Substitution an

= 3 \cdot \int_{0}^{8} \frac{e ^{u}}{16} d u

Entferne die Konstante:

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

= 3 \cdot \frac{1}{16} \cdot \int_{0}^{8} e^{u} d u

Nutze das gemeinsame Integral :

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

= 3 \cdot \frac{1}{16} [e^{u}]_{0}^{8}

Vereinfache

3 \cdot \frac{1}{16} [e^{u}]_{0}^{8} : \frac{3}{16} [e^{u}]_{0}^{8}

= \frac{3}{16} [e^{u}]_{0}^{8}

Berechne die Grenzen:

e^{8} - 1

= \frac{3}{16} (e^{8} - 1)

Vereinfache

= \frac{3 ( e ^{8} - 1 )}{16}

\int_{- \infty}^{- 3} \frac{2}{x + 2} d x

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

\int_{- 4}^{0} \frac{3}{2} x + 6 d x

\int_{- 1}^{1} cos (w x) d x

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