integral from 0 to 4 of x/(sqrt(4+x^2))

Lösung

\int_{0}^{4} \frac{x}{4 + x ^{2}} d x

2 (5 - 1)

Dezimale

2.47213 \dots

Schritte zur Lösung

\int_{0}^{4} \frac{x}{4 + x ^{2}} d x

Wende U-Substitution an

= \int_{4}^{20} \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_{4}^{20} \frac{1}{u} d u

Wende die Potenzregel an

= \frac{1}{2} [2 u^{\frac{1}{2}}]_{4}^{20}

Wende Radikal Regel an:

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

= \frac{1}{2} [2 u]_{4}^{20}

Berechne die Grenzen:

45 - 4

= \frac{1}{2} (45 - 4)

Vereinfache

= 2 (5 - 1)

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