integral from pi/6 to pi/3 of cot^4(x)

Lösung

\int_{\frac{π}{6}}^{\frac{π}{3}} cot^{4} (x) d x

\frac{3 3 π + 16}{18 3}

Dezimale

1.03679 \dots

Schritte zur Lösung

\int_{\frac{π}{6}}^{\frac{π}{3}} cot^{4} (x) d x

Wende integrale Reduktion an

= - [\frac{cot ^{3} ( x )}{3}]_{\frac{π}{6}}^{\frac{π}{3}} - \int_{\frac{π}{6}}^{\frac{π}{3}} cot^{2} (x) d x

\int_{\frac{π}{6}}^{\frac{π}{3}} cot^{2} (x) d x = - \frac{π}{6} - \frac{1}{3} + 3

= - [\frac{cot ^{3} ( x )}{3}]_{\frac{π}{6}}^{\frac{π}{3}} - (- \frac{π}{6} - \frac{1}{3} + 3)

Vereinfache

- [\frac{cot ^{3} ( x )}{3}]_{\frac{π}{6}}^{\frac{π}{3}} - (- \frac{π}{6} - \frac{1}{3} + 3) : - [\frac{1}{3} cot^{3} (x)]_{\frac{π}{6}}^{\frac{π}{3}} + \frac{π}{6} + \frac{1}{3} - 3

= - [\frac{1}{3} cot^{3} (x)]_{\frac{π}{6}}^{\frac{π}{3}} + \frac{π}{6} + \frac{1}{3} - 3

Berechne die Grenzen:

\frac{1}{9 3} - 3

= - (\frac{1}{9 3} - 3) + \frac{π}{6} + \frac{1}{3} - 3

Vereinfache

= \frac{3 3 π + 16}{18 3}

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