integral from 0 to pi of sin^2(n)x

Lösung

\int_{0}^{π} sin^{2} (n) x d x

sin^{2} (n) \frac{π ^{2}}{2}

Schritte zur Lösung

\int_{0}^{π} sin^{2} (n) x d x

Entferne die Konstante:

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

= sin^{2} (n) \cdot \int_{0}^{π} x d x

Wende die Potenzregel an

= sin^{2} (n) [\frac{x ^{2}}{2}]_{0}^{π}

Berechne die Grenzen:

\frac{π ^{2}}{2}

= sin^{2} (n) \frac{π ^{2}}{2}

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