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Beliebt Rechnen >

integral from 0 to 3/11 of 1/(121x^2+9)

Lösung

\int_{0}^{\frac{3}{11}} \frac{1}{121 x ^{2} + 9} d x

Lösung

\frac{π}{132}

+1

Dezimale

0.02379 \dots

Schritte zur Lösung

\int_{0}^{\frac{3}{11}} \frac{1}{121 x ^{2} + 9} d x

Wende integrale Substitution an

= \int_{0}^{1} \frac{1}{33 ( u ^{2} + 1 )} d u

Entferne die Konstante:

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

= \frac{1}{33} \cdot \int_{0}^{1} \frac{1}{u ^{2} + 1} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u ^{2} + 1} d u = arctan (u)

= \frac{1}{33} [arctan (u)]_{0}^{1}

Berechne die Grenzen:

\frac{π}{4}

= \frac{1}{33} \cdot \frac{π}{4}

Vereinfache

= \frac{π}{132}

Graph

Beliebte Beispiele

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\int_{1}^{3} (2 + x) d x

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\int_{0}^{7} x^{3} d x