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Beliebt Rechnen >

integral from pi/6 to pi/4 of sin(4t)

Lösung

\int_{\frac{π}{6}}^{\frac{π}{4}} sin (4 t) d t

Lösung

\frac{1}{8}

+1

Dezimale

0.125

Schritte zur Lösung

\int_{\frac{π}{6}}^{\frac{π}{4}} sin (4 t) d t

Wende U-Substitution an

= \int_{\frac{2 π}{3}}^{π} sin (u) \frac{1}{4} d u

Entferne die Konstante:

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

= \frac{1}{4} \cdot \int_{\frac{2 π}{3}}^{π} sin (u) d u

Nutze das gemeinsame Integral :

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

= \frac{1}{4} [- cos (u)]_{\frac{2 π}{3}}^{π}

Berechne die Grenzen:

\frac{1}{2}

= \frac{1}{4} \cdot \frac{1}{2}

Vereinfache

= \frac{1}{8}

Graph

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