integral from 0 to 1 of sin(wx)

Lösung

\int_{0}^{1} sin (w x) d x

\frac{- cos ( w ) + 1}{w}

Schritte zur Lösung

\int_{0}^{1} sin (w x) d x

Wende U-Substitution an

= \int_{0}^{w} \frac{sin ( u )}{w} d u

Entferne die Konstante:

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

= \frac{1}{w} \cdot \int_{0}^{w} sin (u) d u

Nutze das gemeinsame Integral :

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

= \frac{1}{w} [- cos (u)]_{0}^{w}

Berechne die Grenzen:

- cos (w) + 1

= \frac{1}{w} (- cos (w) + 1)

Vereinfache

= \frac{- cos ( w ) + 1}{w}

\int_{\frac{π}{6}}^{\frac{π}{4}} csc^{2} (x) d x

\int_{0}^{π} x \cdot sin (3 x) d x

\int_{1}^{2} x e^{4 x^{2}} d x

\int_{2}^{- 2} 4 - x^{2} d x

\int_{0}^{1} sin^{4} (x) cos (x) d x