integral from 0 to 4 of xsin(3x)

Lösung

\int_{0}^{4} x sin (3 x) d x

\frac{1}{9} sin (12) - \frac{4}{3} cos (12)

Dezimale

- 1.18475 \dots

Schritte zur Lösung

\int_{0}^{4} x sin (3 x) d x

Wende die partielle Integration an

= [- \frac{1}{3} x cos (3 x) - \int - \frac{1}{3} cos (3 x) d x]_{0}^{4}

\int - \frac{1}{3} cos (3 x) d x = - \frac{1}{9} sin (3 x)

= [- \frac{1}{3} x cos (3 x) - (- \frac{1}{9} sin (3 x))]_{0}^{4}

Vereinfache

= [- \frac{1}{3} x cos (3 x) + \frac{1}{9} sin (3 x)]_{0}^{4}

Berechne die Grenzen:

\frac{1}{9} sin (12) - \frac{4}{3} cos (12)

= \frac{1}{9} sin (12) - \frac{4}{3} cos (12)

\int_{0}^{2 x} 2 x y^{3} - x d y

\int_{- 1}^{1} ∣ x ∣ sin (x) d x

\int_{0}^{\frac{π}{2}} x sin (3 x) d x

\int_{0}^{4 π} ∣ sin (x) ∣ d x

\int_{0}^{2} 4 t^{2} + 1 d t