integral from 0 to 5 of t/(sqrt(11+t^2))

Lösung

\int_{0}^{5} \frac{t}{11 + t ^{2}} d t

6 - 11

Dezimale

2.68337 \dots

Schritte zur Lösung

\int_{0}^{5} \frac{t}{11 + t ^{2}} d t

Wende U-Substitution an

= \int_{11}^{36} \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_{11}^{36} \frac{1}{u} d u

Wende die Potenzregel an

= \frac{1}{2} [2 u^{\frac{1}{2}}]_{11}^{36}

Wende Radikal Regel an:

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

= \frac{1}{2} [2 u]_{11}^{36}

Berechne die Grenzen:

12 - 211

= \frac{1}{2} (12 - 211)

Vereinfache

= 6 - 11

\int_{0}^{2} 25 - x^{2} d x

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