integral from-pi/2 to pi/2 of 4cos(x)

Lösung

\int_{- \frac{π}{2}}^{\frac{π}{2}} 4 cos (x) d x

8

Schritte zur Lösung

\int_{- \frac{π}{2}}^{\frac{π}{2}} 4 cos (x) d x

Entferne die Konstante:

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

= 4 \cdot \int_{- \frac{π}{2}}^{\frac{π}{2}} cos (x) d x

Nutze das gemeinsame Integral :

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

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

Berechne die Grenzen:

2

= 4 \cdot 2

Vereinfache

= 8

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