integral from 0 to pi of xsin(n)x

Lösung

\int_{0}^{π} x sin (n) x d x

sin (n) \frac{π ^{3}}{3}

Schritte zur Lösung

\int_{0}^{π} x sin (n) x d x

Entferne die Konstante:

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

= sin (n) \cdot \int_{0}^{π} xx d x

Vereinfache

xx : x^{2}

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

Wende die Potenzregel an

= sin (n) [\frac{x ^{3}}{3}]_{0}^{π}

Berechne die Grenzen:

\frac{π ^{3}}{3}

= sin (n) \frac{π ^{3}}{3}

\int_{1}^{3} \frac{x ^{2}}{2} d x

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

\int_{0}^{t} sin (t - x) d x

\int_{0}^{1} x^{2} ln (1 + x^{2}) d x

\int_{1}^{3} x^{2} - 2 x + 5 d x