integral from-2 to 2 of (|x|+x)e^{|x|}

Lösung

\int_{- 2}^{2} (∣ x ∣ + x) e^{∣ x ∣} d x

2 (e^{2} + 1)

Dezimale

16.77811 \dots

Schritte zur Lösung

\int_{- 2}^{2} (∣ x ∣ + x) e^{∣ x ∣} d x

Entferne die Extremwerte

= \int_{- 2}^{0} (- x + x) e^{- x} d x + \int_{0}^{2} (x + x) e^{x} d x

\int_{- 2}^{0} (- x + x) e^{- x} d x = 0

\int_{0}^{2} (x + x) e^{x} d x = 2 (e^{2} + 1)

= 0 + 2 (e^{2} + 1)

Vereinfache

= 2 (e^{2} + 1)

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