integral from 0 to 1 of cos(npit)

Lösung

\int_{0}^{1} cos (nπ t) d t

0

Schritte zur Lösung

\int_{0}^{1} cos (nπ t) d t

Wende U-Substitution an

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

Entferne die Konstante:

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

= \frac{1}{πn} \cdot \int_{0}^{πn} cos (u) d u

Nutze das gemeinsame Integral :

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

= \frac{1}{πn} [sin (u)]_{0}^{πn}

Berechne die Grenzen:

0

= \frac{1}{πn} \cdot 0

Vereinfache

= 0

\int_{0}^{1} (2 e^{x}) d x

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