integral from 0 to infinity of ((sin(x))/x)

Lösung

\int_{0}^{\infty} (\frac{sin ( x )}{x}) d x

\frac{π}{2}

Dezimale

1.57079 \dots

Schritte zur Lösung

\int_{0}^{\infty} \frac{sin ( x )}{x} d x

Berechne das unbestimmte Integral:

\int \frac{sin ( x )}{x} d x = Si (x) + C

Berechne die Grenzen:

\int_{0}^{\infty} (\frac{sin ( x )}{x}) d x = \frac{π}{2} - 0

= \frac{π}{2} - 0

Vereinfache

= \frac{π}{2}

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