integral from 0 to pi of sin^4(θ)

Lösung

\int_{0}^{π} sin^{4} (θ) d θ

\frac{3 π}{8}

Dezimale

1.17809 \dots

Schritte zur Lösung

\int_{0}^{π} sin^{4} (θ) d θ

Wende integrale Reduktion an

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

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

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

Vereinfache

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

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

Berechne die Grenzen:

0

= - 0 + \frac{3 π}{8}

Vereinfache

= \frac{3 π}{8}

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