integral from 2 to 5 of (cos(x/(10)))

Lösung

\int_{2}^{5} (cos (\frac{x}{10})) d x

10 (sin (\frac{1}{2}) - sin (\frac{1}{5}))

Dezimale

2.80756 \dots

Schritte zur Lösung

\int_{2}^{5} cos (\frac{x}{10}) d x

Wende U-Substitution an

= \int_{\frac{1}{5}}^{\frac{1}{2}} cos (u) \cdot 10 d u

Entferne die Konstante:

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

= 10 \cdot \int_{\frac{1}{5}}^{\frac{1}{2}} cos (u) d u

Nutze das gemeinsame Integral :

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

= 10 [sin (u)]_{\frac{1}{5}}^{\frac{1}{2}}

Berechne die Grenzen:

sin (\frac{1}{2}) - sin (\frac{1}{5})

= 10 (sin (\frac{1}{2}) - sin (\frac{1}{5}))

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