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Beliebt Rechnen >

integral from 0 to 2 of x/(1+10x^2)

Lösung

\int_{0}^{2} \frac{x}{1 + 10 x ^{2}} d x

Lösung

\frac{1}{20} ln (41)

+1

Dezimale

0.18567 \dots

Schritte zur Lösung

\int_{0}^{2} \frac{x}{1 + 10 x ^{2}} d x

Wende U-Substitution an

= \int_{1}^{41} \frac{1}{20 u} d u

Entferne die Konstante:

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

= \frac{1}{20} \cdot \int_{1}^{41} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{20} [ln ∣ u ∣]_{1}^{41}

Berechne die Grenzen:

ln (41)

= \frac{1}{20} ln (41)

Graph

Beliebte Beispiele

integral from 1 to 8 of (1/x)

\int_{1}^{8} (\frac{1}{x}) d x

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\int_{0}^{2} 4 - x d x

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\int_{- 3}^{1} 8 d x

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integral from 0 to 2-2x of (2x+2y-4)

\int_{0}^{2 - 2 x} (2 x + 2 y - 4) d y