integral from 0 to pi of sin(sqrt(x))

Lösung

\int_{0}^{π} sin (x) d x

2 (sin (π) - π cos (π))

Dezimale

2.66949 \dots

Schritte zur Lösung

\int_{0}^{π} sin (x) d x

Wende U-Substitution an

= \int_{0}^{π} sin (u) \cdot 2 u d u

Entferne die Konstante:

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

= 2 \cdot \int_{0}^{π} sin (u) u d u

Wende die partielle Integration an

= 2 [- u cos (u) - \int - cos (u) d u]_{0}^{π}

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

= 2 [- u cos (u) - (- sin (u))]_{0}^{π}

Vereinfache

= 2 [- u cos (u) + sin (u)]_{0}^{π}

Berechne die Grenzen:

sin (π) - π cos (π)

= 2 (sin (π) - π cos (π))

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