integral from 0 to sqrt(x of)cos(10t)

Lösung

\int_{0}^{x} cos (10 t) d t

\frac{1}{10} sin (10 x)

Schritte zur Lösung

\int_{0}^{x} cos (10 t) d t

Wende U-Substitution an

= \int_{0}^{10 x} cos (u) \frac{1}{10} d u

Entferne die Konstante:

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

= \frac{1}{10} \cdot \int_{0}^{10 x} cos (u) d u

Nutze das gemeinsame Integral :

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

= \frac{1}{10} [sin (u)]_{0}^{10 x}

Berechne die Grenzen:

sin (10 x)

= \frac{1}{10} sin (10 x)

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