integral from 1 to 3 of 1/(sqrt(4x-x^2))

Lösung

\int_{1}^{3} \frac{1}{4 x - x ^{2}} d x

\frac{π}{3}

Dezimale

1.04719 \dots

Schritte zur Lösung

\int_{1}^{3} \frac{1}{4 x - x ^{2}} d x

Vervollständige das Quadrat

4 x - x^{2} : - (x - 2)^{2} + 4

= \int_{1}^{3} \frac{1}{- ( x - 2 ) ^{2} + 4} d x

Wende U-Substitution an

= \int_{- 1}^{1} \frac{1}{- u ^{2} + 4} d u

Trigonometrische Substitution anwenden

= \int_{- \frac{π}{6}}^{\frac{π}{6}} 1 d v

Integral einer Konstanten :

\int a d x = a x

= [1 \cdot v]_{- \frac{π}{6}}^{\frac{π}{6}}

Vereinfache

= [v]_{- \frac{π}{6}}^{\frac{π}{6}}

Berechne die Grenzen:

\frac{π}{3}

= \frac{π}{3}

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