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Beliebt Rechnen >

integral from 0 to 1 of ((9t)/(1+t^2))

Lösung

\int_{0}^{1} (\frac{9 t}{1 + t ^{2}}) d t

Lösung

\frac{9}{2} ln (2)

+1

Dezimale

3.11916 \dots

Schritte zur Lösung

\int_{0}^{1} \frac{9 t}{1 + t ^{2}} d t

Entferne die Konstante:

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

= 9 \cdot \int_{0}^{1} \frac{t}{1 + t ^{2}} d t

Wende U-Substitution an

= 9 \cdot \int_{1}^{2} \frac{1}{2 u} d u

Entferne die Konstante:

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

= 9 \cdot \frac{1}{2} \cdot \int_{1}^{2} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= 9 \cdot \frac{1}{2} [ln ∣ u ∣]_{1}^{2}

Vereinfache

9 \cdot \frac{1}{2} [ln ∣ u ∣]_{1}^{2} : \frac{9}{2} [ln ∣ u ∣]_{1}^{2}

= \frac{9}{2} [ln ∣ u ∣]_{1}^{2}

Berechne die Grenzen:

ln (2)

= \frac{9}{2} ln (2)

Graph

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