integral from 1 to 0 of 3e^x

Lösung

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

- 3 (e - 1)

Dezimale

- 5.15484 \dots

Schritte zur Lösung

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

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{0}^{1} 3 e^{x} d x

Entferne die Konstante:

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

= - 3 \cdot \int_{0}^{1} e^{x} d x

Nutze das gemeinsame Integral :

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

= - 3 [e^{x}]_{0}^{1}

Berechne die Grenzen:

e - 1

= - 3 (e - 1)

\int_{a}^{10 b} 2 s d s

\int_{- 1}^{1} 3 x^{5} - 3 x^{2} - 3 x + 3 d x

\int_{0}^{2} (3 x^{2} e^{2 x^{3}}) d x

\int_{0}^{\frac{π}{8}} sin (4 x) d x

\int_{0}^{8} - t^{2} + 3 t + 32 d t