integral from 0 to 1 of cos^4(x)

Lösung

\int_{0}^{1} cos^{4} (x) d x

\frac{3}{8} (- \frac{1}{4} sin (4) + 1) + cos^{3} (1) sin (1)

Dezimale

0.57867 \dots

Schritte zur Lösung

\int_{0}^{1} cos^{4} (x) d x

Vereinfache

cos^{4} (x) : cos^{3} (x) cos (x)

= \int_{0}^{1} cos^{3} (x) cos (x) d x

Wende die partielle Integration an

= [cos^{3} (x) sin (x) - \int - 3 cos^{2} (x) sin^{2} (x) d x]_{0}^{1}

\int - 3 cos^{2} (x) sin^{2} (x) d x = - \frac{3}{8} (x - \frac{1}{4} sin (4 x))

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

Vereinfache

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

Berechne die Grenzen:

\frac{3}{8} (- \frac{1}{4} sin (4) + 1) + cos^{3} (1) sin (1)

= \frac{3}{8} (- \frac{1}{4} sin (4) + 1) + cos^{3} (1) sin (1)

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