integral from 0 to pi/2 of sin^{10}(x)

Lösung

\int_{0}^{\frac{π}{2}} sin^{10} (x) d x

\frac{63 π}{512}

Dezimale

0.38656 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{2}} sin^{10} (x) d x

Wende integrale Reduktion an

= - [\frac{cos ( x ) sin ^{9} ( x )}{10}]_{0}^{\frac{π}{2}} + \frac{9}{10} \cdot \int_{0}^{\frac{π}{2}} sin^{8} (x) d x

\int_{0}^{\frac{π}{2}} sin^{8} (x) d x = \frac{35 π}{256}

= - [\frac{cos ( x ) sin ^{9} ( x )}{10}]_{0}^{\frac{π}{2}} + \frac{9}{10} \cdot \frac{35 π}{256}

Vereinfache

- [\frac{cos ( x ) sin ^{9} ( x )}{10}]_{0}^{\frac{π}{2}} + \frac{9}{10} \cdot \frac{35 π}{256} : - [\frac{1}{10} sin^{9} (x) cos (x)]_{0}^{\frac{π}{2}} + \frac{63 π}{512}

= - [\frac{1}{10} sin^{9} (x) cos (x)]_{0}^{\frac{π}{2}} + \frac{63 π}{512}

Berechne die Grenzen:

0

= - 0 + \frac{63 π}{512}

Vereinfache

= \frac{63 π}{512}

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