integral from 0 to 8 of x/(sqrt(36+x^2))

Lösung

\int_{0}^{8} \frac{x}{36 + x ^{2}} d x

4

Schritte zur Lösung

\int_{0}^{8} \frac{x}{36 + x ^{2}} d x

Wende U-Substitution an

= \int_{36}^{100} \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_{36}^{100} \frac{1}{u} d u

Wende die Potenzregel an

= \frac{1}{2} [2 u^{\frac{1}{2}}]_{36}^{100}

Wende Radikal Regel an:

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

= \frac{1}{2} [2 u]_{36}^{100}

Berechne die Grenzen:

8

= \frac{1}{2} \cdot 8

Vereinfache

= 4

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