integral from 0 to pi of (4e^x+5sin(x))

Lösung

\int_{0}^{π} (4 e^{x} + 5 sin (x)) d x

4 e^{π} + 6

Dezimale

98.56277 \dots

Schritte zur Lösung

\int_{0}^{π} 4 e^{x} + 5 sin (x) 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}^{π} 4 e^{x} d x + \int_{0}^{π} 5 sin (x) d x

\int_{0}^{π} 4 e^{x} d x = 4 (e^{π} - 1)

\int_{0}^{π} 5 sin (x) d x = 10

= 4 (e^{π} - 1) + 10

Vereinfache

4 (e^{π} - 1) + 10 : 4 e^{π} + 6

= 4 e^{π} + 6