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

Lösung

\int_{0}^{\frac{π}{2}} sin (4 x) d x

0

Schritte zur Lösung

\int_{0}^{\frac{π}{2}} sin (4 x) d x

Wende U-Substitution an

= \int_{0}^{2 π} sin (u) \frac{1}{4} d u

Entferne die Konstante:

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

= \frac{1}{4} \cdot \int_{0}^{2 π} sin (u) d u

Nutze das gemeinsame Integral :

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

= \frac{1}{4} [- cos (u)]_{0}^{2 π}

Berechne die Grenzen:

0

= \frac{1}{4} \cdot 0

Vereinfache

= 0

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

\int_{0}^{1} \frac{x}{1 - x} d x

\int_{e}^{e^{2}} \frac{ln ( x )}{x} d x

\int_{0}^{1} \frac{x ^{2}}{1 + x ^{3}} d x

\int_{0}^{3} x e^{2 x} d x