integral from 0 to (5pi)/6 of cos(2t)

Lösung

\int_{0}^{\frac{5 π}{6}} cos (2 t) d t

- \frac{3}{4}

Dezimale

- 0.43301 \dots

Schritte zur Lösung

\int_{0}^{\frac{5 π}{6}} cos (2 t) d t

Wende U-Substitution an

= \int_{0}^{\frac{5 π}{3}} cos (u) \frac{1}{2} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{0}^{\frac{5 π}{3}} cos (u) d u

Nutze das gemeinsame Integral :

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

= \frac{1}{2} [sin (u)]_{0}^{\frac{5 π}{3}}

Berechne die Grenzen:

- \frac{3}{2}

= \frac{1}{2} (- \frac{3}{2})

Vereinfache

= - \frac{3}{4}

\int_{- 2}^{2} \frac{x}{x + 3} d x

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