integral from 0 to (3pi)/4 of cos(2t)

Lösung

\int_{0}^{\frac{3 π}{4}} cos (2 t) d t

- \frac{1}{2}

Dezimale

- 0.5

Schritte zur Lösung

\int_{0}^{\frac{3 π}{4}} cos (2 t) d t

Wende U-Substitution an

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

Nutze das gemeinsame Integral :

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

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

Berechne die Grenzen:

- 1

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

Vereinfache

= - \frac{1}{2}

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