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Beliebt Rechnen >

integral from 1 to 2 of 2cos(3x)

Lösung

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

Lösung

\frac{2}{3} (sin (6) - sin (3))

+1

Dezimale

- 0.28035 \dots

Schritte zur Lösung

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

Entferne die Konstante:

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

= 2 \cdot \int_{1}^{2} cos (3 x) d x

Wende U-Substitution an

= 2 \cdot \int_{3}^{6} cos (u) \frac{1}{3} d u

Entferne die Konstante:

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

= 2 \cdot \frac{1}{3} \cdot \int_{3}^{6} cos (u) d u

Nutze das gemeinsame Integral :

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

= 2 \cdot \frac{1}{3} [sin (u)]_{3}^{6}

Vereinfache

2 \cdot \frac{1}{3} [sin (u)]_{3}^{6} : \frac{2}{3} [sin (u)]_{3}^{6}

= \frac{2}{3} [sin (u)]_{3}^{6}

Berechne die Grenzen:

sin (6) - sin (3)

= \frac{2}{3} (sin (6) - sin (3))

Graph

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\int_{- 2}^{3} \frac{1}{8} d x

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