integral from 60 to 90 of 1/(4+x^2)

Lösung

\int_{60}^{90} \frac{1}{4 + x ^{2}} d x

\frac{1}{2} (arctan (45) - arctan (30))

Dezimale

0.00555 \dots

Schritte zur Lösung

\int_{60}^{90} \frac{1}{4 + x ^{2}} d x

Wende integrale Substitution an

= \int_{30}^{45} \frac{1}{2 ( u ^{2} + 1 )} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{30}^{45} \frac{1}{u ^{2} + 1} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{2} [arctan (u)]_{30}^{45}

Berechne die Grenzen:

arctan (45) - arctan (30)

= \frac{1}{2} (arctan (45) - arctan (30))

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