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

Lösung

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

5 - 2

Dezimale

0.82185 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{2}^{5} \frac{1}{2 u} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{2}^{5} \frac{1}{u} d u

Wende die Potenzregel an

= \frac{1}{2} [2 u^{\frac{1}{2}}]_{2}^{5}

Wende Radikal Regel an:

a^{\frac{1}{n}} = n a

= \frac{1}{2} [2 u]_{2}^{5}

Berechne die Grenzen:

25 - 22

= \frac{1}{2} (25 - 22)

Vereinfache

= 5 - 2

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