integral from x/2 to x of-sin(x)

Lösung

\int_{\frac{x}{2}}^{x} - sin (x) d x

cos (x) - cos (\frac{x}{2})

Schritte zur Lösung

\int_{\frac{x}{2}}^{x} - sin (x) d x

Entferne die Konstante:

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

= - \int_{\frac{x}{2}}^{x} sin (x) d x

Nutze das gemeinsame Integral :

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

= - [- cos (x)]_{\frac{x}{2}}^{x}

Berechne die Grenzen:

- cos (x) + cos (\frac{x}{2})

= - (- cos (x) + cos (\frac{x}{2}))

Vereinfache

= cos (x) - cos (\frac{x}{2})

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