integral from 0 to pi of (pi-x)sin(nx)

Lösung

\int_{0}^{π} (π - x) sin (n x) d x

\frac{π}{n}

Schritte zur Lösung

\int_{0}^{π} (π - x) sin (n x) d x

Wende die partielle Integration an

= [\frac{1}{n} (- cos (n x) (π - x) - n \cdot \int \frac{1}{n} cos (n x) d x)]_{0}^{π}

\int \frac{1}{n} cos (n x) d x = \frac{1}{n ^{2}} sin (n x)

= [\frac{1}{n} (- cos (n x) (π - x) - n \frac{1}{n ^{2}} sin (n x))]_{0}^{π}

Vereinfache

[\frac{1}{n} (- cos (n x) (π - x) - n \frac{1}{n ^{2}} sin (n x))]_{0}^{π} : [\frac{1}{n} (- cos (n x) (π - x) - \frac{1}{n} sin (n x))]_{0}^{π}

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

Berechne die Grenzen:

\frac{π}{n}

= \frac{π}{n}

\frac{\partial}{\partial x} (x y^{2} - x^{3} y)

d er i v a t i v e f (x) = (2 x^{3} + 3)^{6}

t an g e n t - 2 x^{2}

\int 9 x^{2} - 8 x d x

\int \frac{3}{1 + 9 x ^{2}} d x