integral from 0 to 1 of e^{3t}

Lösung

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

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

Dezimale

6.36184 \dots

Schritte zur Lösung

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

Wende U-Substitution an

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

Entferne die Konstante:

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

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

Nutze das gemeinsame Integral :

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

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

Berechne die Grenzen:

e^{3} - 1

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

Vereinfache

= \frac{e ^{3} - 1}{3}

\int_{0}^{2 π} 4 cos (t) sin (t) d t

\int_{0}^{x} \frac{1}{2} sin (t) d t

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

\int_{0}^{25} - 6 x d x

\int_{0}^{\infty} x^{\frac{1}{2}} d x