integral from 0 to pi/2 of cos(x+2y)

Lösung

\int_{0}^{\frac{π}{2}} cos (x + 2 y) d y

\frac{1}{2} (sin (x + π) - sin (x))

Schritte zur Lösung

\int_{0}^{\frac{π}{2}} cos (x + 2 y) d y

Wende U-Substitution an

= \int_{x}^{x + π} cos (u) \frac{1}{2} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{x}^{x + π} cos (u) d u

Nutze das gemeinsame Integral :

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

= \frac{1}{2} [sin (u)]_{x}^{x + π}

Berechne die Grenzen:

sin (x + π) - sin (x)

= \frac{1}{2} (sin (x + π) - sin (x))

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