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

Lösung

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

\frac{1}{3}

Dezimale

0.33333 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{1}^{4} \frac{1}{6 u} d u

Entferne die Konstante:

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

= \frac{1}{6} \cdot \int_{1}^{4} \frac{1}{u} d u

Wende die Potenzregel an

= \frac{1}{6} [2 u^{\frac{1}{2}}]_{1}^{4}

Wende Radikal Regel an:

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

= \frac{1}{6} [2 u]_{1}^{4}

Berechne die Grenzen:

2

= \frac{1}{6} \cdot 2

Vereinfache

= \frac{1}{3}

\int_{0}^{\frac{6}{7}} \frac{1}{49 x ^{2} + 36} d x

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\int_{1}^{5} \frac{2 x}{x ^{2} - 4} d x

\int_{4}^{7} \frac{1}{x} d x

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