integral from 0 to 2pi of sin^4(θ)

Lösung

\int_{0}^{2 π} sin^{4} (θ) d θ

\frac{3 π}{4}

Dezimale

2.35619 \dots

Schritte zur Lösung

\int_{0}^{2 π} sin^{4} (θ) d θ

Wende integrale Reduktion an

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

\int_{0}^{2 π} sin^{2} (θ) d θ = π

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

Berechne die Grenzen:

0

= - 0 + \frac{3}{4} π

Vereinfache

= \frac{3 π}{4}

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