integral from 0 to pi of cos^6(x)

Lösung

\int_{0}^{π} cos^{6} (x) d x

\frac{5 π}{16}

Dezimale

0.98174 \dots

Schritte zur Lösung

\int_{0}^{π} cos^{6} (x) d x

Wende integrale Reduktion an

= [\frac{sin ( x ) cos ^{5} ( x )}{6}]_{0}^{π} + \frac{5}{6} \cdot \int_{0}^{π} cos^{4} (x) d x

\int_{0}^{π} cos^{4} (x) d x = \frac{3 π}{8}

= [\frac{sin ( x ) cos ^{5} ( x )}{6}]_{0}^{π} + \frac{5}{6} \cdot \frac{3 π}{8}

Vereinfache

[\frac{sin ( x ) cos ^{5} ( x )}{6}]_{0}^{π} + \frac{5}{6} \cdot \frac{3 π}{8} : [\frac{1}{6} cos^{5} (x) sin (x)]_{0}^{π} + \frac{5 π}{16}

= [\frac{1}{6} cos^{5} (x) sin (x)]_{0}^{π} + \frac{5 π}{16}

Berechne die Grenzen:

0

= 0 + \frac{5 π}{16}

Vereinfache

= \frac{5 π}{16}

y^{^{'}} = 0.285 (1 - y)

100 y^{^{''}} = 0

x \to 3 lim (5 x^{2})

\frac{d}{d x} (x^{- \frac{2}{3}} (x + 5))

\frac{d}{d x} (\frac{6 x + 8 x ^{2}}{( 3 + 8 x ) ^{2}})