integral from pi/4 to pi/2 of cot^3(x)

Lösung

\int_{\frac{π}{4}}^{\frac{π}{2}} cot^{3} (x) d x

\frac{1}{2} - \frac{1}{2} ln (2)

Dezimale

0.15342 \dots

Schritte zur Lösung

\int_{\frac{π}{4}}^{\frac{π}{2}} cot^{3} (x) d x

Wende integrale Reduktion an

= - [\frac{cot ^{2} ( x )}{2}]_{\frac{π}{4}}^{\frac{π}{2}} - \int_{\frac{π}{4}}^{\frac{π}{2}} cot (x) d x

\int_{\frac{π}{4}}^{\frac{π}{2}} cot (x) d x = \frac{1}{2} ln (2)

= - [\frac{cot ^{2} ( x )}{2}]_{\frac{π}{4}}^{\frac{π}{2}} - \frac{1}{2} ln (2)

Berechne die Grenzen:

- \frac{1}{2}

= - (- \frac{1}{2}) - \frac{1}{2} ln (2)

Vereinfache

= \frac{1}{2} - \frac{1}{2} ln (2)

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