integral from 0 to l of cos((npix)/l)

Lösung

\int_{0}^{l} cos (\frac{nπ x}{l}) d x

0

Schritte zur Lösung

\int_{0}^{l} cos (\frac{nπ x}{l}) d x

Wende U-Substitution an

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

Wende U-Substitution an

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

Entferne die Konstante:

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

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

Nutze das gemeinsame Integral :

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

= \frac{1}{πn} l [sin (v)]_{0}^{πn}

Berechne die Grenzen:

0

= \frac{1}{πn} l \cdot 0

Vereinfache

= 0

\int_{1}^{9} 6 u d u

\int_{1}^{2} (x - 1)^{3} d x

\int_{2}^{4} 25 - x^{2} d x

\int_{0}^{π} t \cdot cos (n t) d t

\int_{0}^{4} x e^{3 x} d x