integral from 0 to 1 of x/(sqrt(x^2+3))

Lösung

\int_{0}^{1} \frac{x}{x ^{2} + 3} d x

2 - 3

Dezimale

0.26794 \dots

Schritte zur Lösung

\int_{0}^{1} \frac{x}{x ^{2} + 3} d x

Wende U-Substitution an

= \int_{3}^{4} \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_{3}^{4} \frac{1}{u} d u

Wende die Potenzregel an

= \frac{1}{2} [2 u^{\frac{1}{2}}]_{3}^{4}

Wende Radikal Regel an:

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

= \frac{1}{2} [2 u]_{3}^{4}

Berechne die Grenzen:

4 - 23

= \frac{1}{2} (4 - 23)

Vereinfache

= 2 - 3

\int_{0}^{7} x^{2} d x

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\int_{0}^{\frac{π}{4}} arctan (x) d x