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Beliebt Rechnen >

integral from-1/3 to 1/3 of 1/(1+9x^2)

Lösung

\int_{- \frac{1}{3}}^{\frac{1}{3}} \frac{1}{1 + 9 x ^{2}} d x

Lösung

\frac{π}{6}

+1

Dezimale

0.52359 \dots

Schritte zur Lösung

\int_{- \frac{1}{3}}^{\frac{1}{3}} \frac{1}{1 + 9 x ^{2}} d x

Wende integrale Substitution an

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

Entferne die Konstante:

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

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

Nutze das gemeinsame Integral :

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

= \frac{1}{3} [arctan (u)]_{- 1}^{1}

Berechne die Grenzen:

\frac{π}{2}

= \frac{1}{3} \cdot \frac{π}{2}

Vereinfache

= \frac{π}{6}

Graph

Beliebte Beispiele

y^'=(2xy)/(x^2+1),y(1)=6

y^{^{'}} = \frac{2 x y}{x ^{2} + 1}, y (1) = 6

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\int \frac{1}{cos ( x ) sin ( x )} d x