integral from 0 to 10 of sin((pix)/(10))

Lösung

\int_{0}^{10} sin (\frac{π x}{10}) d x

\frac{20}{π}

Dezimale

6.36619 \dots

Schritte zur Lösung

\int_{0}^{10} sin (\frac{π x}{10}) d x

Wende U-Substitution an

= \int_{0}^{π} sin (u) \frac{10}{π} d u

Entferne die Konstante:

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

= \frac{10}{π} \cdot \int_{0}^{π} sin (u) d u

Nutze das gemeinsame Integral :

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

= \frac{10}{π} [- cos (u)]_{0}^{π}

Berechne die Grenzen:

2

= \frac{10}{π} \cdot 2

Vereinfache

= \frac{20}{π}

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