integral from pi/6 to pi/3 of 6cos(x)

Lösung

\int_{\frac{π}{6}}^{\frac{π}{3}} 6 cos (x) d x

3 (3 - 1)

Dezimale

2.19615 \dots

Schritte zur Lösung

\int_{\frac{π}{6}}^{\frac{π}{3}} 6 cos (x) d x

Entferne die Konstante:

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

= 6 \cdot \int_{\frac{π}{6}}^{\frac{π}{3}} cos (x) d x

Nutze das gemeinsame Integral :

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

= 6 [sin (x)]_{\frac{π}{6}}^{\frac{π}{3}}

Berechne die Grenzen:

\frac{3}{2} - \frac{1}{2}

= 6 (\frac{3}{2} - \frac{1}{2})

Vereinfache

= 3 (3 - 1)

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