integral from-1 to 3 of x/(1+|x|)

Lösung

\int_{- 1}^{3} \frac{x}{1 + ∣ x ∣} d x

- ln (2) + 2

Dezimale

1.30685 \dots

Schritte zur Lösung

\int_{- 1}^{3} \frac{x}{1 + ∣ x ∣} d x

Entferne die Extremwerte

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

\int_{- 1}^{0} \frac{x}{1 - x} d x = - 1 + ln (2)

\int_{0}^{3} \frac{x}{1 + x} d x = 3 - 2 ln (2)

= - 1 + ln (2) + 3 - 2 ln (2)

Vereinfache

= - ln (2) + 2

\int_{0}^{2} k x d x

\int_{- 1}^{4} 3 x + 4 - x^{2} d x

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\int_{- \frac{2 π}{3}}^{\frac{π}{3}} sin (x) d x