integral from 0 to 1 of xsin(n)pix

Lösung

\int_{0}^{1} x sin (n) π x d x

\frac{π}{3} sin (n)

Schritte zur Lösung

\int_{0}^{1} x sin (n) π x d x

Entferne die Konstante:

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

= sin (n) π \cdot \int_{0}^{1} xx d x

Vereinfache

xx : x^{2}

= sin (n) π \cdot \int_{0}^{1} x^{2} d x

Wende die Potenzregel an

= sin (n) π [\frac{x ^{3}}{3}]_{0}^{1}

Berechne die Grenzen:

\frac{1}{3}

= sin (n) π \frac{1}{3}

Vereinfache

= \frac{π}{3} sin (n)

\int_{5}^{10} x^{2} + 5 d x

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