integral from pi/4 to pi/2 of 7cot^3(x)

Lösung

\int_{\frac{π}{4}}^{\frac{π}{2}} 7 cot^{3} (x) d x

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

Dezimale

1.07398 \dots

Schritte zur Lösung

\int_{\frac{π}{4}}^{\frac{π}{2}} 7 cot^{3} (x) d x

Entferne die Konstante:

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

= 7 \cdot \int_{\frac{π}{4}}^{\frac{π}{2}} cot^{3} (x) d x

Wende integrale Reduktion an

= 7 (- [\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)

= 7 (- [\frac{cot ^{2} ( x )}{2}]_{\frac{π}{4}}^{\frac{π}{2}} - \frac{1}{2} ln (2))

Berechne die Grenzen:

- \frac{1}{2}

= 7 (- (- \frac{1}{2}) - \frac{1}{2} ln (2))

Vereinfache

= 7 (\frac{1}{2} - \frac{1}{2} ln (2))

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