integral from-pi/2 to pi/2 of cos(2θ)

Lösung

\int_{- \frac{π}{2}}^{\frac{π}{2}} cos (2 θ) d θ

0

Schritte zur Lösung

\int_{- \frac{π}{2}}^{\frac{π}{2}} cos (2 θ) d θ

Wende U-Substitution an

= \int_{- π}^{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_{- π}^{π} cos (u) d u

Nutze das gemeinsame Integral :

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

= \frac{1}{2} [sin (u)]_{- π}^{π}

Berechne die Grenzen:

0

= \frac{1}{2} \cdot 0

Vereinfache

= 0

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\int_{1}^{\infty} e^{- n}