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Beliebt Rechnen >

integral from 0 to pi of 8sin^4(x)

Lösung

\int_{0}^{π} 8 sin^{4} (x) d x

Lösung

3 π

+1

Dezimale

9.42477 \dots

Schritte zur Lösung

\int_{0}^{π} 8 sin^{4} (x) d x

Entferne die Konstante:

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

= 8 \cdot \int_{0}^{π} sin^{4} (x) d x

Wende integrale Reduktion an

= 8 (- [\frac{cos ( x ) sin ^{3} ( x )}{4}]_{0}^{π} + \frac{3}{4} \cdot \int_{0}^{π} sin^{2} (x) d x)

\int_{0}^{π} sin^{2} (x) d x = \frac{π}{2}

= 8 (- [\frac{cos ( x ) sin ^{3} ( x )}{4}]_{0}^{π} + \frac{3}{4} \cdot \frac{π}{2})

Vereinfache

8 (- [\frac{cos ( x ) sin ^{3} ( x )}{4}]_{0}^{π} + \frac{3}{4} \cdot \frac{π}{2}) : - 8 [\frac{1}{4} sin^{3} (x) cos (x)]_{0}^{π} + 3 π

= - 8 [\frac{1}{4} sin^{3} (x) cos (x)]_{0}^{π} + 3 π

Berechne die Grenzen:

0

= - 8 \cdot 0 + 3 π

Vereinfache

= 3 π

Graph

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