integral from 0 to 2 of 5(1-e^y)

Lösung

\int_{0}^{2} 5 (1 - e^{y}) d y

5 (- e^{2} + 3)

Dezimale

- 21.94528 \dots

Schritte zur Lösung

\int_{0}^{2} 5 (1 - e^{y}) d y

Entferne die Konstante:

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

= 5 \cdot \int_{0}^{2} 1 - e^{y} d y

Wende die Summenregel an:

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

= 5 (\int_{0}^{2} 1 d y - \int_{0}^{2} e^{y} d y)

\int_{0}^{2} 1 d y = 2

\int_{0}^{2} e^{y} d y = e^{2} - 1

= 5 (2 - (e^{2} - 1))

Vereinfache

= 5 (- e^{2} + 3)

\int_{0}^{1} \frac{ln ( x )}{x ^{\frac{1}{3}}} d x

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