integral from-pi to pi of x*sin(x)

Lösung

\int_{- π}^{π} x \cdot sin (x) d x

2 π

Dezimale

6.28318 \dots

Schritte zur Lösung

\int_{- π}^{π} x sin (x) d x

Wende die partielle Integration an

= [- x cos (x) - \int - cos (x) d x]_{- π}^{π}

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

= [- x cos (x) - (- sin (x))]_{- π}^{π}

Vereinfache

= [- x cos (x) + sin (x)]_{- π}^{π}

Berechne die Grenzen:

2 π

= 2 π

\int_{1}^{10} x \cdot \frac{2}{81} (x - 1) d x

\int_{3}^{9} \frac{9}{x} - 1 d x

\int_{- 1}^{1} - 2 x d x

\int_{0}^{\frac{1}{2}} r 1 - r^{2} d r

\int_{- \infty}^{x} e^{- x} d x