integral from 1 to infinity of 7/(1+x^2)

Lösung

\int_{1}^{\infty} \frac{7}{1 + x ^{2}} d x

\frac{7 π}{4}

Dezimale

5.49778 \dots

Schritte zur Lösung

\int_{1}^{\infty} \frac{7}{1 + x ^{2}} d x

Berechne das unbestimmte Integral:

\int \frac{7}{1 + x ^{2}} d x = 7 arctan (x) + C

Berechne die Grenzen:

\int_{1}^{\infty} \frac{7}{1 + x ^{2}} d x = 7 \cdot \frac{π}{2} - 7 \cdot \frac{π}{4}

= 7 \cdot \frac{π}{2} - 7 \cdot \frac{π}{4}

Vereinfache

= \frac{7 π}{4}

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