integral from 0 to 4 of 1/(25x^2+9)

Lösung

\int_{0}^{4} \frac{1}{25 x ^{2} + 9} d x

\frac{1}{15} arctan (\frac{20}{3})

Dezimale

0.09479 \dots

Schritte zur Lösung

\int_{0}^{4} \frac{1}{25 x ^{2} + 9} d x

Wende integrale Substitution an

= \int_{0}^{\frac{20}{3}} \frac{1}{15 ( u ^{2} + 1 )} d u

Entferne die Konstante:

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

= \frac{1}{15} \cdot \int_{0}^{\frac{20}{3}} \frac{1}{u ^{2} + 1} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{15} [arctan (u)]_{0}^{\frac{20}{3}}

Berechne die Grenzen:

arctan (\frac{20}{3})

= \frac{1}{15} arctan (\frac{20}{3})

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