integral from 0 to 0.5 of sin(pix)

Lösung

\int_{0}^{0.5} sin (π x) d x

\frac{1}{π}

Dezimale

0.31830 \dots

Schritte zur Lösung

\int_{0}^{0.5} sin (π x) d x

Wende U-Substitution an

= \int_{0}^{1.57079 \dots} sin (u) \frac{1}{π} d u

Entferne die Konstante:

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

= \frac{1}{π} \cdot \int_{0}^{1.57079 \dots} sin (u) d u

Nutze das gemeinsame Integral :

\int sin (u) d u = - cos (u)

= \frac{1}{π} [- cos (u)]_{0}^{1.57079 \dots}

Berechne die Grenzen:

1

= \frac{1}{π} \cdot 1

Vereinfache

= \frac{1}{π}

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