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

Lösung

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

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

Dezimale

6.36184 \dots

Schritte zur Lösung

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

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_{- 5}^{5} \frac{9}{x ^{3}} d x

\int_{- 1}^{1} - 3 x^{2} d x

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

\int_{1}^{4} (\frac{x}{8} - \frac{3}{x}) d x

\int_{0}^{1} \frac{( - x + 1 ) ^{3}}{6} d x