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Beliebt Rechnen >

integral from 0 to 3 of 1/(sqrt(6v-v^2))

Lösung

\int_{0}^{3} \frac{1}{6 v - v ^{2}} d v

Lösung

\frac{π}{2}

+1

Dezimale

1.57079 \dots

Schritte zur Lösung

\int_{0}^{3} \frac{1}{6 v - v ^{2}} d v

Vervollständige das Quadrat

6 v - v^{2} : - (v - 3)^{2} + 9

= \int_{0}^{3} \frac{1}{- ( v - 3 ) ^{2} + 9} d v

Wende U-Substitution an

= \int_{- 3}^{0} \frac{1}{- u ^{2} + 9} d u

Trigonometrische Substitution anwenden

= \int_{- \frac{π}{2}}^{0} 1 d w

Integral einer Konstanten :

\int a d x = a x

= [1 \cdot w]_{- \frac{π}{2}}^{0}

Vereinfache

= [w]_{- \frac{π}{2}}^{0}

Berechne die Grenzen:

\frac{π}{2}

= \frac{π}{2}

Graph

Beliebte Beispiele

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