integral from 0 to 3 of e^x-1

Lösung

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

e^{3} - 4

Dezimale

16.08553 \dots

Schritte zur Lösung

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

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

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

= e^{3} - 1 - 3

Vereinfache

= e^{3} - 4

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

\int_{0}^{1} (5 x^{2} - 8 x + 3) d x

\int_{5}^{13} (5 - x) (x - 13) d x

\int_{0}^{\infty} \frac{1}{3 ^{x}} d x

\int_{0}^{6} (6) d x