integral from 0 to pi/2 of xsin(4x)

Lösung

\int_{0}^{\frac{π}{2}} x sin (4 x) d x

- \frac{π}{8}

Dezimale

- 0.39269 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{2}} x sin (4 x) d x

Wende die partielle Integration an

= [\frac{1}{4} (- x cos (4 x) - 4 \cdot \int - \frac{1}{4} cos (4 x) d x)]_{0}^{\frac{π}{2}}

\int - \frac{1}{4} cos (4 x) d x = - \frac{1}{16} sin (4 x)

= [\frac{1}{4} (- x cos (4 x) - 4 (- \frac{1}{16} sin (4 x)))]_{0}^{\frac{π}{2}}

Vereinfache

[\frac{1}{4} (- x cos (4 x) - 4 (- \frac{1}{16} sin (4 x)))]_{0}^{\frac{π}{2}} : [\frac{1}{4} (- x cos (4 x) + \frac{1}{4} sin (4 x))]_{0}^{\frac{π}{2}}

= [\frac{1}{4} (- x cos (4 x) + \frac{1}{4} sin (4 x))]_{0}^{\frac{π}{2}}

Berechne die Grenzen:

- \frac{π}{8}

= - \frac{π}{8}

t a y l or 4 x

\int 3 + s (s + 1)^{2} d s

d er i v a t i v e f (x) = ln (25 sin^{2} (x))

d er i v a t i v e y (X) = 0.167 X

x \to 0 lim (x^{9 s i n (x)})