integral from-2 to 0 of-cos((npix)/2)

Lösung

\int_{- 2}^{0} - cos (\frac{nπ x}{2}) d x

0

Schritte zur Lösung

\int_{- 2}^{0} - cos (\frac{nπ x}{2}) d x

Entferne die Konstante:

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

= - \int_{- 2}^{0} cos (\frac{nπ x}{2}) d x

Wende U-Substitution an

= - \int_{- πn}^{0} \frac{2 cos ( u )}{πn} d u

Entferne die Konstante:

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

= - \frac{2}{πn} \cdot \int_{- πn}^{0} cos (u) d u

Nutze das gemeinsame Integral :

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

= - \frac{2}{πn} [sin (u)]_{- πn}^{0}

Berechne die Grenzen:

0

= - \frac{2}{πn} \cdot 0

Vereinfache

= 0

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