integral from pi/6 to pi/3 of cos(3x)

Lösung

\int_{\frac{π}{6}}^{\frac{π}{3}} cos (3 x) d x

- \frac{1}{3}

Dezimale

- 0.33333 \dots

Schritte zur Lösung

\int_{\frac{π}{6}}^{\frac{π}{3}} cos (3 x) d x

Wende U-Substitution an

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

Nutze das gemeinsame Integral :

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

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

Berechne die Grenzen:

- 1

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

Vereinfache

= - \frac{1}{3}

\int_{- 2 π}^{2 π} 5 sin (x) d x

\int_{0}^{0.5} sin (π t) d t

\int_{0}^{x^{2}} 4 x cos (y) d y

\int_{- \frac{π}{4}}^{\frac{π}{4}} 6 tan^{4} (x) d x

\int_{1}^{0} 6 x (4 - x) d x