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Beliebt Rechnen >

integral from 0 to pi/2 of cos^4(x)

Lösung

\int_{0}^{\frac{π}{2}} cos^{4} (x) d x

Lösung

\frac{3 π}{16}

+1

Dezimale

0.58904 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{2}} cos^{4} (x) d x

Vereinfache

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

= \int_{0}^{\frac{π}{2}} 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}^{\frac{π}{2}}

\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}^{\frac{π}{2}}

Vereinfache

[cos^{3} (x) sin (x) - (- \frac{3}{8} (x - \frac{1}{4} sin (4 x)))]_{0}^{\frac{π}{2}} : [\frac{1}{32} (32 cos^{3} (x) sin (x) + 3 (4 x - sin (4 x)))]_{0}^{\frac{π}{2}}

= [\frac{1}{32} (32 cos^{3} (x) sin (x) + 3 (4 x - sin (4 x)))]_{0}^{\frac{π}{2}}

Berechne die Grenzen:

\frac{3 π}{16}

= \frac{3 π}{16}

Graph

Beliebte Beispiele

integral of (5x+3)/(x^2+4x+4)

\int \frac{5 x + 3}{x ^{2} + 4 x + 4} d x

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\frac{d}{d x} (2^{3^{x^{2}}})

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\int x^{2} x^{3} + 29 d x

(1-x^2)y^'+x(y-1)=-x^3

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