integral from 0 to pi/3 of (sin(3x))

Lösung

\int_{0}^{\frac{π}{3}} (sin (3 x)) d x

\frac{2}{3}

Dezimale

0.66666 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{3}} sin (3 x) d x

Wende U-Substitution an

= \int_{0}^{π} sin (u) \frac{1}{3} d u

Entferne die Konstante:

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

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

Nutze das gemeinsame Integral :

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

= \frac{1}{3} [- cos (u)]_{0}^{π}

Berechne die Grenzen:

2

= \frac{1}{3} \cdot 2

Vereinfache

= \frac{2}{3}

\int_{0}^{\frac{π}{3}} cos (x) - 0.5 d x

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\int_{0}^{3} x^{2} - 4 x + 3 d x

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\int_{0}^{5} \frac{1}{1 - x ^{2}} d x